TOGLIATTI, Russia -- In a karate studio in this provincial Russian town, the lesson seemed as much about politics as about martial arts.
Mikhail D. Prokhorov, the once-secretive Russian billionaire who now leads a political party, was a guest instructor for a class of young men.
"Your body should be soft like water," Mr. Prokhorov, 48, explained as he rounded his 6-foot-8 frame and then, improbably, rolled on his back along the top of a hardwood bench. If he grimaced, nobody saw it.
"When you were a child, you knew how to relax and roll," he went on. "If even one muscle tenses, you will get hurt. Be like water. At first, it is uncomfortable for you, but then it will become uncomfortable for your opponent."
Outside the karate class, flexibility, if not a Zen-like self-restraint in the face of serious affronts from the Kremlin, have defined Mr. Prokhorov's low-profile role in Russian politics this summer.
The oligarch who is best known in the United States for owning the Brooklyn Nets basketball franchise and spending lavishly on players, leads a small pro-business party in Russia called Civic Platform. It is fielding candidates in 30 or so local elections -- for City Council, regional legislature, mayor -- here in September.
The most important race is for mayor of Moscow, where a street protest leader, Aleksei A. Navalny, who is a galvanizing and mesmerizing figure running as much for his own freedom as for public office, is the most watched candidate.
A court convicted Mr. Navalny on what were widely seen as trumped-up charges, but released him pending appeal, allowing him to run in the mayoral race; a strong showing could sway the authorities to commute the sentence.
Mr. Prokhorov, in contrast, says he is testing how much can be achieved within President Vladimir V. Putin's political system without resorting to civil disobedience, and risking prosecution, though he does not rule out that he could be arrested.
"In Russia, nobody is guaranteed against becoming a beggar or a prisoner," he said, in an interview aboard his Gulfstream jet, headed to a campaign event in Togliatti, in central Russia.
Mostly his role in politics seems to define the line, some invisible, shifting isocline of permissibility, of what will be allowed of independent political figures here today. It has not been encouraging.
So far much of the challenge has been keeping his candidates for regional political races out of jail.
A day after he chose the mayor of the city of Yaroslavl, Yevgeny R. Urlashov, to lead a slate in regional elections, the police arrested Mr. Urlashov on corruption charges.
Mr. Prokhorov took this in stride. He said that a court would have to sort out the merits of the case, but that he would keep Mr. Urlashov at the top of the candidate list for the September elections, even as he languished in jail.
"You need to stand by your comrades," Mr. Prokhorov explained to an audience of university students during the campaign swing here. But that gesture soon became irrelevant: the authorities in Yaroslavl simply disqualified the whole slate of party members from the ballot, on a technicality.
Elsewhere, election officials barred Mr. Prokhorov's candidates for regional governor, also on paperwork pretexts, in the region of Vladimir near Moscow and in Zabaikal territory, on the border with China.
And no sooner had his highest-profile prospect, Yevgeny Roizman, announced his candidacy for mayor of the city of Yekaterinburg, than he was under investigation. The police are looking into whether Mr. Roizman stole icons.
The problem with the election in Russia this summer, Mr. Prokhorov said, is that "law enforcement is becoming a factor in the electoral process."
And if there is a man in Russia with something to lose, after all, it is he.
One of the richest entrepreneurs on earth, with a fortune that Forbes has estimated at $13 billion, he lives boyhood dreams: he is a sports lover who owns his own basketball team, a fan of rock music who jets to festivals when his schedule allows.
He travels with a martial arts master, an eerily calm figure who dresses, ninjalike, in black, and can do sit-ups while balanced on a soccer ball.
He is known to be so fond of parties that his entourage once took to calling him "the Holiday Man," and a few years back, soon after selling out of the Siberian mine Norilsk Nickel at the top of the market, he gleefully rented the Aurora battleship in St. Petersburg for a party for bankers, its decks crowded with head-spinning models.
Yet his political intentions are serious enough that Mr. Prokhorov shifted ownership of the Nets to a Russian company this year, to comply with a law limiting the foreign assets public officials can own.
Igor M. Bunin, president of the Center for Political Technologies, a political and business consultancy in Moscow, said Mr. Prokhorov is calibrating his political ambitions to avoid too open a challenge to Mr. Putin, in spite of provocative arrests of his candidates.
Sometimes, his approach seems dry. Civic Platform, for example, has been derided as a "party of lawyers."
"He is speaking between the lines," Mr. Bunin said. "He is saying he is an alternative to Putin, a possible successor. But he cannot commit to a stronger, more confrontational strategy. This is limiting his potential."
Mr. Prokhorov, for his part, said that Russia is hardly as monolithic as it appears from afar, or even as the Kremlin would like it to seem, and that success is possible through the ballot box and worth being patient for. Mr. Prokhorov won 7 percent of the vote when he ran for president in 2012.
"A process of schisms in the elite is under way today," he said. "In the Kremlin, in the government, in Parliament, in the regions and at the end of the day, in the kitchens of this country, politics has returned to Russia."
The splintering, he said, creates openings within the electoral process, even if they are long shots. Of politics, he said, "I like the strategy of it. I like to form systematic programs, and create solutions."
Mr. Prokhorov said his goal in regional elections is a second-place finish in the City Council in Togliatti and solid enough results elsewhere to form factions in regional legislatures. This, he said, would lay the foundation for a solid showing by his party in parliamentary elections in 2016.
This article originally appeared in The New York Times.