Higher algebraic K-theory of group actions with finite stabilizers

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over afield 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 GL(n)-action and finally to a split torus action.