A federal grand jury in Michigan on Thursday indicted four engineering managers at German carmaker Audi in connection with a widening diesel emissions cheating scandal.

Richard Bauder, Axel Eiser, Stefan Knirsch and Carsten Nagel were named in a 12-count indictment charging them with violating the federal Clean Air Act, as well as wire fraud and conspiracy.

A Justice Department spokesman told The Associated Press that none of the four was in custody and they were believed to be in Germany. A spokesman for Volkswagen, which owns Audi, told the AP he could not comment about whether the men still work for the company.

It's unlikely any of the German citizens will face a U.S. judge in the case. Germany's constitution forbids extraditing its citizens other than to another European Union member state or to an international court.

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The indictment alleges that Bauder, Eiser, Knirsch and Nagel helped to develop and implement so-called "defeat devices" designed to cheat emissions tests for three-liter diesel engines.

According to court documents, Bauder was head of Audi's diesel engine development department in Neckarsulm, Germany, from 2002 until around February of 2012. Eiser had the same position in Ingolstadt, Germany, from 2009 until around May of 2013. Knirsch had the same position in Ingolstadt from May 2013 to May of 2015, and also was a member of Audi's management board. Nagel was head of Audi's Engine Registration and Testing in Neckarsulm from 2002 through February 2017.

The indictment said the employees realized they could not create a diesel engine with a storage tank for fluid to treat diesel emissions "within the design constraints imposed by Audi, including the need for a large trunk and high-end sound system." So, they and co-conspirators allegedly designed software to cheat on the emissions tests so they could get by with a smaller tank for the fluid.

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Tests conducted by Nagel and others found that nitrogen oxide emissions from vehicles with the diesel engines were up to 22 times above the U.S. limit, the indictment stated. The results were shared with Knirsch and Nagel, according to the indictment.

The document also alleged that the suspects covered up the defeat devices when dealing with U.S. officials, knowing that "if they had told the truth and disclosed the [device's] existence ... Audi would not have obtained the requisite [compliance] Certificates ... and would not have been legally permitted to sell the Subject Vehicles in the United States."

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Thursday's indictments mean 13 VW employees have been charged in the scandal, in which VW used software on about 600,000 vehicles to turn pollution controls on during EPA tests and turn them off while on the road. Two have pleaded guilty and were sentenced to jail time, while six others, including former VW CEO Martin Winterkorn, have remained in Germany.

Volkswagen pleaded guilty in 2016 to criminal charges in the scandal and is set to pay more than $30 billion in penalties and lawsuit settlement costs.

Fox News' Jake Gibson and The Associated Press contributed to this report.