| Abstract: | In 1992, Blanc and Brylinski showed the following property for a  -adic group  , called the ``abstract Selberg principle': the orbital integrals on conjugacy classes of non-compact elements of the Hattori rank of a finitely generated projective smooth representation of  vanish. The proof is by explicit computations of ``low' level ( and  cyclic and Hochschild cohomologies. Here we intend to show that this property is actually a direct consequence of two facts: Clozel's integration formula (which leads us to assume the defining characteristic to be zero) and the triviality of the action of unramified characters on the  of  (which is also proven here, using a standard  -theoretic argument due to Grothendieck). |
