Higher algebraic K-theory of group actions with finite stabilizers

Abstract

We prove a decomposition theorem for the equivariant $K$-theory of actions of affine group schemes $G$ of finite type over a field on regular separated Noetherian algebraic spaces, under the hypothesis that the actions have finite geometric stabilizers and satisfy a rationality condition together with a technical condition that holds, for example, for $G$ abelian or smooth. We reduce the problem to the case of a ${\rm GL}\sb n$-action and finally to a split torus action.