RENO, Nev. — Apple, the world’s most profitable tech company, doesn’t design iPhones here. It doesn’t run AppleCare customer service here. And it doesn’t manufacture MacBooks or iPads here.

Yet, with a handful of employees in a small Reno office in a company subsidiary named Braeburn Capital, Apple has done something central to its corporate strategy: It has avoided millions of dollars in taxes in 21 states.

In this way, Apple serves as a window on how technology giants have taken advantage of tax codes made for an industrial age.

Apple’s headquarters are in Cupertino, Calif. By putting an office to collect and invest the company’s profits out of Reno, just 200 miles away, Apple sidesteps state income taxes on some of those gains.

California’s corporate tax rate is 8.84 percent. Nevada’s? Zero.

Setting up an office in Reno is just one of many legal methods Apple uses to reduce its worldwide tax bill by billions of dollars each year.

As it has in Nevada, Apple has created subsidiaries in low-tax countries like Ireland, the Netherlands, Luxembourg and the British Virgin Islands — some little more than a letterbox in Luxembourg or an anonymous office here — that help cut the taxes it pays around the world.

Almost every major corporation tries to minimize its taxes, of course. For Apple, the savings are especially alluring because the company’s profits are so high. Wall Street analysts predict Apple could earn up to $45.6 billion in its current fiscal year — which would be a record for any U.S. business.

Braeburn is a variety of apple that is simultaneously sweet and tart. When someone in the United States buys an iPhone, iPad or other Apple product, a portion of the profits from that sale is often deposited into accounts controlled by Braeburn and then invested in stocks, bonds or other financial instruments, company executives say. Some profits from those investments are shielded from California tax authorities by virtue of Braeburn’s Nevada address.

Since founding Braeburn in 2006, Apple has earned more than $2.5 billion in interest and dividend income on its cash reserves and investments around the globe. What’s more, Braeburn allows Apple to lower its taxes in other states because many of those jurisdictions use formulas that reduce what is owed when a company’s financial management occurs elsewhere.

While Apple’s Reno office helps the company avoid state taxes, its international subsidiaries — particularly the company’s assignment of sales and patent royalties to other nations — help reduce taxes owed to the U.S. and other governments.

The Luxembourg subsidiary, named iTunes S.ar.l., has just a few dozen employees, according to corporate documents filed in that nation and a current executive. But when customers across Europe, Africa or the Middle East — and potentially elsewhere — download a song, television show or app, the sale is recorded in this small country, according to current and former executives.

The country has promised to tax the payments collected by Apple and numerous other tech corporations at low rates if they route transactions through Luxembourg. Taxes that would have otherwise gone to the governments of Britain, France, the United States go to Luxembourg instead.

In 2011, iTunes S.ar.l.’s revenue exceeded $1 billion, according to an Apple executive, representing roughly 20 percent of iTunes’ worldwide sales.

The digital economy

Some profits at companies like Apple, Google, Amazon, Hewlett-Packard and Microsoft derive not from physical goods but royalties on intellectual property, like the patents on software that makes devices work.

Other times, the products themselves are digital, like downloaded songs. It is much easier for businesses with royalties and digital products to move profits to low-tax countries than it is, say, for grocery stores or automakers. A downloaded application, unlike a car, can be sold from anywhere.

The growing digital economy presents a conundrum for U.S. lawmakers overseeing corporate taxation: Though technology is now one of the nation’s largest and most valued industries, many tech companies are among the least taxed, according to government and corporate data.

Even among tech companies, Apple’s rates are low. And Apple, say former executives, has been particularly talented at identifying legal tax loopholes and hiring accountants who are known for their innovation. Apple was a pioneer of an accounting technique known as the “Double Irish with a Dutch Sandwich,” which reduced taxes by routing profits through two Irish subsidiaries — today named Apple Operations International and Apple Sales International — and the Netherlands and then to the Caribbean. In 2004, Ireland, a nation of less than 5 million, was home to more than one-third of Apple’s worldwide revenues, according to company filings.

Without such tactics, Apple’s federal tax bill in the U.S. most likely would have been $2.4 billion higher last year, according to a recent study by a former Treasury Department economist, Martin Sullivan. As it stands, the company paid cash taxes of $3.3 billion around the world on its reported profits of $34.2 billion last year, a tax rate of 9.8 percent. By comparison, Wal-Mart last year paid worldwide cash taxes of $5.9 billion on its booked profits of $24.4 billion, a tax rate of 24 percent, which is about average for non-tech companies.

The sums paid by Apple and other tech corporations is a point of contention in the company’s backyard.

A mile and a half from Apple’s Cupertino headquarters is De Anza College — a community college that Steve Wozniak, one of Apple’s founders, attended from 1969 to 1974. Because of the state budget crisis, De Anza has cut more than a thousand courses and 8 percent of its faculty since 2008.

Now, De Anza faces a budget gap so large it is confronting a “death spiral,” school President Brian Murphy told the faculty in January. Apple, of course, is not responsible for the state’s financial shortfall. But its tax policies are seen by officials like Murphy as symptomatic of why the crisis exists.

“I just don’t understand it,” he said in an interview. “I’ll bet every person at Apple has a connection to De Anza. Their kids swim in our pool. Their cousins take classes here. They drive past it every day, for Pete’s sake. But then they do everything they can to pay as few taxes as possible.”

Apple’s response

As a comment on the its tax practices, Apple provided this statement (which has been edited down) to The New York Times:

“Over the past several years, we have created an incredible number of jobs in the United States. The vast majority of our global work force remains in the U.S., with more than 47,000 full-time employees in all 50 states. By focusing on innovation, we’ve created entirely new products and industries. … We manufacture parts in the U.S. and export them around the world, and U.S. developers create apps that we sell in over 100 countries. … Apple also pays an enormous amount of taxes which help our local, state and federal governments. In the first half of fiscal year 2012 our U.S. operations have generated almost $5 billion in federal and state income taxes. … We have contributed to many charitable causes but have never sought publicity for doing so. Our focus has been on doing the right thing.”

On the Web

This is part of a New York Times series examining the challenges posed by increasingly globalized high-tech industries. For today’s full story, plus graphics showing Apple’s techniques, go to www.nytimes.com.