THE people who killed Boris Nemtsov, a liberal politician, on February 27th, did not expect to be arrested. That was clear from their impudence.

Having shot Mr Nemtsov in the back, in the heart of Moscow, they did not cross the river to leave the city centre. Instead, they circled the Kremlin, passed the Duma, Russia’s parliament, and turned into a well-lit, half-pedestrian street. They did not even burn their getaway car.

Such brazen behaviour raised suspicions that the killers might be Chechen hitmen, of the sort who work for Ramzan Kadyrov, the president of Chechnya, who has hitherto been a big friend of Russia’s president, Vladimir Putin. Now some are wondering whether the seemingly solid pact between Mr Putin and Mr Kadyrov (pictured above) may have become too costly for the Russian leader.

An ex-warlord, Mr Kadyrov was plucked out of obscurity by the Russian leader and put in charge of the once mutinous Caucasian republic, succeeding his father who had been assassinated. Mr Putin has let Mr Kadyrov ignore Russian laws and settle scores freely. In the past decade, Chechnya has virtually become a separate Islamic state under Mr Kadyrov’s rule. He has his own 20,000-strong army, his own (informal) tax system and his own religious laws.

As Russia’s strongest regional leader, Mr Kadyrov extends his influence right across the country. His security men have special status in Moscow. After officers of the Federal Security Service (FSB), the alma mater of Mr Putin, arrested a group of Mr Kadyrov’s men over kidnappings, torture and extortion in the capital, the suspects walked free.

Several nasty murders have highlighted Chechen impunity. When Anna Politkovskaya, a brave reporter, was killed in 2006, the main suspect went to Chechnya and lived near Mr Kadyrov. He was jailed for life after a probe by the dead woman’s colleagues, but those who ordered the killing were not named. After the death of Natalia Estemirova, a human-rights activist slain in Chechnya after threats from Mr Kadyrov, nobody was held responsible.

One of Mr Kadyrov’s old rivals, Ruslan Yamadaev, was shot dead in rush-hour traffic, next to a public building in Moscow. His brother, who had led a pro-Russian unit against Georgia, was assassinated in Dubai, where police issued a warrant for Adam Delimkhanov, Mr Kadyrov’s right-hand man and relative. In 2009 Mr Kadyrov’s ex-security guard, who had spoken of torture and executions carried out by his old bosses, was killed in Vienna.

Few were surprised on March 8th when Alexander Bortnikov, head of the FSB, announced that five men had been detained over the murder of Mr Nemtsov, including Zaur Dadaev, an ex-commander of the “North battalion”, made up of Mr Kadyrov’s irregular forces. Indeed, the only person who seemed shocked was Mr Kadyrov, who has made odd statements since the Nemtsov killing. On the day of the murder, he wrote on his Instagram account that Western spooks were to blame. After Mr Dadaev’s arrest, he spoke out again: “I knew Zaur as a true patriot…he is devoted to Russia and was always ready to give his life for it. Even if the court confirms his guilt…he could not have taken a step against Russia.” (Soon after, Mr Dadaev retracted his confession.)

In his Instagram statement, Mr Kadyrov hinted that Mr Nemtsov might have been killed for condemning the terrorist attack on the French weekly Charlie Hebdo. The Chechen leader’s own reaction was different: he led a vast rally in his capital Grozny against Charlie Hebdo, not the killing of its staff. The Russian security services claim that Mr Dadaev and his men planned and carried out Mr Nemtsov’s murder. That raises many questions. Few observers believe that anything involving Chechen fighters occurs without Mr Kadyrov’s and Mr Delimkhanov’s knowledge. But the same probably goes for the FSB, whose agents trailed Mr Nemtsov. As ever in Russia there are more theories than facts. Some wonder whether the FSB has exploited the killing to settle scores with Mr Kadyrov. There is no love lost between senior Russian military and security officers and the Kadyrov camp. Russian officers in Chechnya resent the political authority and conspicuous wealth of Chechens who were once their foes. In 2010 Russian forces accused the North battalion of betraying them in a clash with rebels. While swearing loyalty to Mr Putin, at home Mr Kadyrov boasts of having won independence not by fighting Moscow but by milking it. Mr Kadyrov’s reaction to the arrest of Mr Dadaev suggests a hard struggle between forces previously united around Mr Putin: the FSB and his Chechen friends. As Novaya Gazeta, a liberal paper, wrote: “Two pillars of Kremlin support bashed their heads and are now moving in the opposite directions, forcing the Kremlin to choose which is a true patriot of Russia.”

The stakes are high; Mr Putin is trying to preserve at least the appearance of stability, and this week went ahead with a planned award to Mr Kadyrov. Should the Chechen leader lose Kremlin support, he and his male progeny may be at risk because he has many "blood enemies". Mr Putin also needs Mr Kadyrov to keep order in Chechnya.

But the bond is unstable. “The contract between Kadyrov and Putin—money in exchange for loyalty—is coming to an end. Where will Mr Kadyrov’s 20,000 men go? What will they demand? How will they act? When will they come to Moscow?” Those rhetorical questions were posed by Mr Nemtsov shortly before his death.