Construction of a toll road from Jakarta to Lido, the planned location for a theme park linked to companies with business interests tied to US President Donald Trump, in West Java province. A billion-dollar Indonesian real estate development with ties to Donald Trump has become the latest project in China's globe-spanning Belt and Road infrastructure project -- just as Washington and Beijing are tussling over trade.

HONG KONG — In Thailand, a theater rigged with hydraulic seats will give moviegoers the sensation of flight. In Australia, an indoor ski slope is going up near the beaches of the Gold Coast. In the Czech Republic, a spa with Chinese medicine is under construction in the southern wine country.

All three projects fall under Beijing's ambitious effort to build geopolitical and economic ties around the world — and all three stray from its original mission.

Under President Xi Jinping, Beijing has pledged trillions of dollars toward the construction of roads, power plants and ports in Asia, Africa and Europe through its Belt and Road initiative. The program envisions big, critical infrastructure projects, backed and blessed by the Chinese government, as the path to winning friends and spreading influence.

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But five years in, smaller, less impactful projects are finding cover under the umbrella of Belt and Road, using the program to slip past restrictions on foreign investment. Beijing has discouraged, and in some cases blocked, deals in the real estate and entertainment industries, part of a broader crackdown on profligate spending by Chinese companies overseas.

As the economy shows signs of strain, Chinese officials are sounding caution about the program, taking a closer look at the financing of deals and the number of projects underway.

That hasn't discouraged some companies.

"There are wacky deals that occur under the banner of Belt and Road because this is how every entrepreneur signals that they are in line with the leadership's political objectives," said Arthur Kroeber, managing director of Gavekal Dragonomics, an independent economic research firm.

"It certainly is a very capacious arena for opportunists, that's for sure," Mr. Kroeber added.

In addition to the Chinese-medicine spa in the Czech Republic, there are plans for Chinese cultural centers and theme parks in Hungary, Italy, the Philippines, Russia, Serbia and Vietnam. One construction firm used the Belt and Road plan to justify a deal to build an amusement park in an Indonesian complex that includes a Trump hotel and golf course.

In addition to straying into entertainment venues, the Belt and Road mission is sprawling geographically. Initially focused on countries along the ancient trade route that once carried travelers including Marco Polo east, the program's official scope has been extended to Africa and South America.

Australia, however, has yet to be included. That is not stopping Songcheng Performance Development, the company building the indoor ski slope, part of a huge amusement park and entertainment complex on about 100 acres of land along the eastern Gold Coast.

"We will offer local cultural park performances such as the story of how Captain Cook discovered Australia," Zhang Xian, the chief executive of Songcheng, recently told investors.

The park, called Australia Legend Kingdom, would seem to combine every sector now subject to a government-imposed freeze: Beijing has tried to clamp down on splashy overseas entertainment, sports and real estate projects by big Chinese conglomerates.

China's Ministry of Culture, though, has named Australia Legend Kingdom a top priority.

In China, Songcheng operates 30 amusement parks with roller coaster rides as well as productions showcasing the cultures of various Chinese ethnic minorities. The company also owns several theme hotels, including one that has replicated a rain forest and another that has fashioned itself as an alternative to the Maldives, except it is on a lake.

The company had long harbored ambitions to expand into Australia, according to Roland Evans, Songcheng's representative there. It spotted an opportunity when President Xi announced the Belt and Road plan in 2013.

Songcheng's plans for the park have not been finalized, but an early proposal includes condominiums for as many as 2,000 residents, and theaters to accommodate musicals and shows about Chinese and Australian history. The company wants the indoor ski hill to be the world's biggest.

Supporters of the myriad cultural projects that fall under the Belt and Road umbrella — and there are many such proponents in China — argue that amusement parks and theaters can underpin China's diplomatic push much as ports and infrastructure do.

"One of the goals is cultural exchange along the Belt and Road to improve our soft power," said Chen Shaofeng, vice dean of the Institute for Cultural Industries at Peking University. "It also provides a strategic support for economic cooperation."

Those are lofty goals for what critics say is basically big-ticket spending overseas.

Some companies involved in the initiative have said that they receive preferential financing from state-backed banks. Others say they are getting government support to help train employees and promote the new business ventures overseas.

Betop Entertainment, which is building the sense-of-flight theater in Thailand, has been successful in getting political buy-in for its project.

Its new theater will be in the beach resort town of Pattaya and will feature scenes of Thailand. It will be the company's first venture outside China, where it owns so-called flying theaters — viewers are strapped into hydraulic chairs that shake and rattle as images fly overhead — in 27 cities, said Li Dan, a company official.

"It fits the policy" of the Belt and Road initiative, Ms. Li noted. "It is best to go in the same direction as government policies."

There are pitfalls to using the Belt and Road name, though. Some Chinese companies have begun to face hurdles with their projects overseas.

RiseSun Real Estate Development has been trying to build a sprawling spa and Chinese-medicine complex in Pasohlavky, a small town in the South Moravia region of the Czech Republic. A government mock-up of the plans, first announced during a state visit to China by the Czech president, Milos Zeman, in 2015, shows more than two dozen buildings along the banks of the Nove Mlyny reservoirs.

But the project has come under local scrutiny.

The publicly listed Chinese company has said that while construction for the spa had not yet started, it was "definitely in the process of being approved." Officials in Pasohlavky offer a different account, saying that RiseSun is only one of multiple groups of investors interested in buying the land.

The local authorities say they have yet to make a final decision. Some residents have expressed unease about a Chinese investor, said Martina Dominova, the town's mayor.

They have watched closely as a drama plays out in Prague, the Czech capital, involving the Chinese company CEFC China Energy. Several years ago, CEFC scooped up a handful of Czech businesses, including part of a bank, a brewery and even a soccer team. Then, this year, the founder of CEFC suddenly disappeared, prompting concerns about the fate of the companies it had bought in the Czech Republic.

"The town hall even received hateful messages," Ms. Dominova said. "They have accused us of selling off the republic to the Chinese."