BERLIN — German authorities on Monday detained the chief executive of Volkswagen’s Audi division, Rupert Stadler, as part of a probe into manipulation of emissions controls. The move follows a search last week of Stadler’s private residence, ordered by Munich prosecutors investigating the manager on suspicion of fraud and indirect improprieties with documents. “Audi CEO Rupert Stadler was provisionally arrested this morning,” the company said in a statement.