On the Mixed Tate property and the motivic class of the classifying stack of a finite group

Abstract

Let G be a finite group, and let {B C G} the class of its classifying stack B C G in Ekedahl's Grothendieck ring of algebraic C-stacks K 0 (Stacks C ). We show that if B C G has the mixed Tate property, the invariants H i ({B C G}) defined by T. Ekedahl are zero for all i = 0. We also extend Ekedahl's construction of these invariants to fields of positive characteristic.