European Commissioner for Competition Margrethe Vestager speaks during a debate on the European Union’s Apple ruling in back taxes at the European Parliament in Strasbourg, France, on Sept. 14. (Frederick Florin/AFP/Getty Images)

In a year of surging anger about the modern globalized economy, one woman may be the best equipped to defuse tensions — and she does her work from a sprawling bureaucratic office building in the heart of Brussels.

More than almost anyone else in the 500-million-person league that is the European Union, Margrethe Vestager, the E.U. official in charge of competition, has the ability to shape perceptions of an institution that is under attack as never before. As angry voters take to the polls on both sides of the Atlantic amid a surging feeling that the system is rigged, the Dane’s mission is to ensure that the little guy has a chance against vast multinational companies.

Because the European Union is the largest economic bloc in the world, Vestager’s investigations touch powerful players across the globe. She has taken on Google and the Kremlin, and just slapped Apple with a gargantuan fine. She has McDonald’s and Facebook in her crosshairs. And she does it all while knitting toy elephants that she bestows on rivals and allies alike.

If she is successful, her efforts could reverberate across Europe, delivering a tough message that Brussels is able to deliver concrete benefits to citizens. But if she overreaches, she could be seen as just another unelected bureaucrat dictating terms to nations trapped within a union that increasingly is seen as causing more strife than comfort.

“The benefits of globalization do not trickle down automatically,” Vestager said in an interview in her brightly decorated office. “It takes politics to make sure that there is a benefit.”

Vestager’s highest-profile judgment came in late summer, when she announced that Apple had improperly avoided $14.2 billion in payments to Ireland based on a years-long tax deal. The company denies any wrongdoing and plans to appeal.

The decision has also come under heavy criticism from the Obama administration, which says that Vestager is twisting competition law and impounding tax revenue that the United States sees as its own. 

Vestager “appears to be adopting an entirely new legal theory and applying it retroactively in a broad and sweeping manner,” Treasury Secretary Jack Lew wrote this year.

And the Irish government worries that the ruling could upend the country’s business model, which has attracted investment in recent years by offering a low-tax, English-speaking home for businesses that want a European toehold.

But the announcement — timed in part to dominate the news as Europe returned from its languorous August holidays — sent a message to ordinary Europeans that powerful companies would not be able to negotiate sweetheart tax deals out of reach of normal citizens. In an era in which blockbuster international trade deals are under fire from opponents who say they neglect all but the strongest business interests, the investigation could make voters sit up and take notice.

Margrethe Vestager. (Jasper Juinen)

“Vestager has a strong will to go after these cases,” said Georgios Petropoulos, an expert on the topic at Bruegel, a Brussels-based policy think tank. “She’s not afraid of these big multinationals.”

The crossfire has not fazed Vestager, a veteran of political power plays in her native Denmark who helped inspire the main character in the hit TV show “Borgen,” her nation’s version of “House of Cards.”

“If my tax rate went down from 0.05 percent to 0.005 percent, I should have felt maybe I should have had a second look at my tax bill,” Vestager said at a combative news conference in which she announced the Apple ruling.

‘Follow the rules’

Vestager, 48, was Denmark’s deputy prime minister and economy minister before arriving in Brussels in late 2014 as the competition commissioner. She is one of 28 E.U. cardinals whose rank is approximately equal to that of a U.S. Cabinet secretary. Her office is unusually powerful inside the E.U., which typically shares regulatory responsibilities between national governments and Brussels. In the field of competition, however, E.U. regulators have unparalleled powers to enforce bloc-wide rules, meaning they can challenge nations and companies and serve as a rare example of the E.U. delivering concrete benefits to citizens.

“Antitrust is really very special in the commission’s having important powers of decision where it doesn’t have to refer back to national governments,” said Alec Burnside, a managing partner at the Brussels office of the Cadwalader law firm, who focuses on E.U. competition issues.

Vestager shies away from lofty notions about saving the European Union, preferring to focus on the more concrete tasks of her portfolio. 

“It’s not in my mission to work against Euroskepticism; it’s my mission to work for fair markets,” she said. But she boils down her sometimes dry, technical work into elemental terms that connect easily with ordinary voters. “In antitrust, what is at stake is in some ways as old as Adam and Eve, because it is about greed, to get more,” she said. 

“Few people think about politics every day,” she said. “But they are in the market every day” — either by working at a job or buying vegetables at the grocery store.

The daughter of two Lutheran pastors, Vestager grew up in a small town in Denmark’s flatlands. She has said a defining memory of her childhood was the sound of cars rolling up the driveway at all hours of the day, as guests came to ask for help. She tried to preserve that focus on listening to others when she entered politics in her 20s.

But listening to others does not mean agreeing with them, and many who have tangled with her say that she is steely once she has made up her mind. On a coffee table in her Brussels office is a cast of a hand with an upraised middle finger, which was given to her by a group of Danish unions enraged by her efforts to curb unemployment benefits. She says she keeps it as a reminder that political decisions will inevitably upset some people.

Those who have worked with her say that her style comes from her experience leading a niche pro-Europe political party, the centrist Social Liberals, in Denmark’s fragmented political system.

In such a party, which typically focuses on a few pet issues, “your job is not to persuade the majority of the people to do something specific,” said Henrik Kjerrumgaard, one of Vestager’s advisers when she was in Danish government. “You can allow yourself to say things that make people angry. Because when someone gets angry, you know you’ve communicated with them in a pure and direct way.”

That no-nonsense style may be helping to shift opinions in some Euroskeptic countries — beginning with Vestager’s own. Denmark is famously skittish about handing power to Brussels, and much like Britain, it agreed to join the European Union only if it was allowed to opt out of a host of issues.

After British voters made the startling decision in June to leave the European Union, many looked at Denmark as a possible next candidate for a departure. Instead, the desire to leave the European Union has decreased, according to opinion polls.

Part of that is due to Vestager’s work, observers say.

“A lot of people who didn’t like her while she was in Denmark like her now because they say, ‘Wow, she’s doing what people think the E.U. should do,’ ” said Elisabet Svane, a Danish political journalist who wrote a biography of Vestager. “It’s quite practical. She’s saying: ‘You’re not following the rules? Follow the rules.’ A lot of E.U. policy is out in the skies, and this is very down-to-earth.”

“She’s doing more good for the European Union now in Denmark than if she had still been in Denmark,” Svane said.