For Marriott, it was the wording of a survey emailed to members of its rewards club. At fashion brand Zara, it was a drop-down menu on its website. And for Audi, it was a presentation at the German carmaker's annual meeting that showed a map of China that excluded Taiwan and parts of Tibet.
All three drew a backlash from the Chinese government. And in the course of a single week, so did more than two dozen other international corporations — including Delta Air Lines, Qantas and Medtronic — for listing Taiwan, Hong Kong, Tibet and Macau as separate countries.
The Chinese government, further extending its political reach on the Web and through social media, demanded public apologies from the companies. In Marriott's case, the government also complained that a U.S.-based employee "liked" a tweet favoring Tibetan independence. The government forced the company to shut down all six of its Chinese websites and apps for one week.
All of the companies have moved to mollify Beijing — and their Chinese customers. "It was an inadvertent error with no business or political intention, and we apologize for the mistake," a spokeswoman for Delta said in an email. "As one of our most important markets, we are fully committed to China and our Chinese customers."
"This is a huge mistake, probably one of the biggest in my career," Craig S. Smith, president and managing director of Marriott's Asia-Pacific office, was quoted as saying in the state-owned China Daily.
To China experts, the striking thing about the episode isn't just the substance of the dispute but the desperate tone of the company's apology.
"Mr. Smith's self-abasement would be comical if it weren't dangerous," said Robert Daly, director of the Wilson Center's Kissinger Institute on China and the United States. "His apology is so abject that it could well become a standard which Beijing requires all future offenders of China to meet."
The efforts by Beijing to curtail free speech at companies doing business with China fit into a larger narrative about the nature of Chinese relations abroad. In recent months, China has also sought to support pro-Beijing campus groups and has warned Chinese students abroad against involvement in groups critical of China.
Once American scholars spoke of the virtue of U.S. cultural and economic "soft power" that sought to build support for American ideals around the world. A December report by the National Endowment for Democracy suggested another term for China and Russia, which it said were projecting "sharp power" that relies on coercion without any effort to "win hearts and minds."
"As China's power and influence grows, corporations will have to ask themselves the same question governments have had to: To what degree do the economic benefits of working with China run counter to the values and principles these companies uphold?" said Ely Ratner, a senior fellow for China studies at the Council on Foreign Relations. "The question becomes whether or not these companies want to be complicit in Chinese authoritarianism."
Failure to follow the official line has consequences. The Chinese newspaper Global Times said that a "netizen" had discovered Marriott's Mandarin-language survey — which listed Tibet, Hong Kong, Macau and Taiwan as options on a question asking customers their countries of residence — and was calling for a boycott of the company. A China National Tourism Administration official was quoted by Xinhua, the state news agency, as saying no activities that challenge China's "legal red lines" would be permitted.
"We welcome foreign corporations' investment and operation in China," Lu Kang, a spokesman for the ministry of foreign affairs, said at a media briefing last week, according to the Financial Times. "Meanwhile, they should abide by China's laws and respect Chinese people's national feelings."
Marriott, which has been aggressively expanding in China in recent years, says it is implementing an "eight-point rectification plan" to prevent future mishaps. The word "rectification" carries extra significance in China because Mao Zedong used rectification campaigns to consolidate his hold on the Chinese Communist Party and indoctrinate its members.
The company took down the survey "immediately," terminated the contract with the Canadian firm that wrote the survey and initiated a review of its materials, including the company's websites, according to a Marriott spokeswoman. The Bethesda-based hotelier is also taking disciplinary action against the employee who used a corporate Twitter account to "like" a post supporting Tibetan independence from China.
"To regain confidence and trust, the first thing is to admit the mistake, then fix it, and it would come back slowly as we prove we really mean what we say," Smith, who has worked for Marriott for 30 years, was quoted as saying in China Daily.
A number of major companies, including Apple and Audi, have acquiesced to China's censorship laws and other demands in recent years, experts said. Apple last year removed more than 670 apps — including messaging apps such as Skype and virtual private networks, which would allow users to bypass government-imposed firewalls — from its Chinese App Store.
Apple's chief executive, Tim Cook, has talked about the importance of China's market to Apple's business strategy and its determination to stay there. "We believe in engaging with governments even when we disagree," he said in August.
He traveled to China in December and appeared at China's World Internet Conference. "The theme of this conference — developing a digital economy for openness and shared benefits — is a vision we at Apple share," Cook said there. "We are proud to have worked alongside many of our partners in China to help build a community that will join a common future in cyberspace."
As for other tech giants, Google's search engine and Facebook's social media platform have been cordoned off from Chinese customers. (Google does have three offices in the country.)
"This kind of policing has been going on for a long time, but it used to be handled much more discreetly," said Sean Miner, a fellow at the Atlantic Council who specializes in China. "Now, though, China is overtly using its economic leverage to publicly shame companies that it believes are crossing the line."
While China has sought to shape debates across digital borders, it remains sensitive about what is said about its own physical borders. Hong Kong and Macau are officially part of China, although they have their own political systems. (Traveling between Hong Kong, Macau and China requires a passport.) Tibet is ruled by China, although some Tibetans say that it is an independent country and that the Dalai Lama is its leader. Self-governing Taiwan, meanwhile, has its own robust democracy and military. China, however, claims it as a province.
"What if a Chinese enterprise listed Alaska or Hawaii as an independent country rather than a state of the United States?" an editorial in China Daily asked. "It would definitely be considered as having infringed on the sovereignty and territorial integrity of the United States."
"Marriott International respects and supports the sovereignty and territorial integrity of China," chief executive Arne Sorenson wrote in a statement on the company's website.
"We don't support anyone who subverts the sovereignty and territorial integrity of China and we do not intend in any way to encourage or incite any such people or groups," he added. "We recognize the severity of the situation and sincerely apologize."
Some China watchers said that Marriott failed to do what the U.S. government learned to do in the 1970s when it was normalizing relations with China: An element of constructive ambiguity can be used to sidestep the question of Taiwan's relationship with Beijing. The United States recognized one China but maintained downgraded relations with Taiwan.
"People say that Marriott kowtowed," said Scott Kennedy, deputy director of China studies at the Center for Strategic and International Studies. "Kowtow" derives from a Chinese phrase for "knocking one's head" on the floor, as people did when bowing to the emperor.
"Having to use a crisis management approach and respond publicly gives it that flavor," Kennedy added. "Yet the place they end up is not really any different from where any government with diplomatic relations ends up: recognize the 'one China' policy and tiptoe around the sovereignty issue and engage in enough ambiguity to have unofficial relations with Taiwan."
From time to time, companies have learned this the hard way. More than 20 years ago, for example, the mobile phone company Nokia listed Taiwan and Hong Kong as among the countries where its products were available.
Today, the Chinese government also can use social media to stir nationalist sentiment among customers of companies that misstep.
More sophisticated firms sidestep sensitive issues with Tibet and Taiwan by referring to them as markets or regions. That, Kennedy said, "probably would have created enough ambiguity."
The Chinese market, which accounted for 19 percent of Marriott's global growth at the end of 2017, is increasingly important to the company. The hotelier is working hard to woo the country's growing middle class. It has opened more than 240 hotels — many of them high-end resorts — in China over the past five years as it looks to familiarize a growing population of travelers with the 91-year-old brand.
Altogether, the company has more than 300 hotels in China. And those properties are increasingly lucrative: During the first nine months of 2017, Marriott said revenue per available room, a key industry metric, rose 8.4 percent in greater China, compared with 1.5 percent in North America and 2.6 percent worldwide.
"China is the biggest single market for us outside the U.S.," Sorenson said at an industry conference in June. "We're opening in excess of one [hotel] a week in China."
By emailing the survey, "Marriott was looking for a way to understand its customers, and it learned a different lesson from the one it was expecting to," Kennedy said. "The challenge is how to be respectful but not obsequious."
Two decades ago, rapid economic modernization and foreign investment was thought to be linked to political liberalization. That no longer appears to be the case.
"I think there was a hope that as China grew, there would be less state intervention in the economy — but the current trend is exactly the opposite," Ratner said. "The party has a larger role than before in economic decisions."
Simon Denyer contributed to this report from Beijing.