$K_0$ of invariant rings and nonabelian $H^1$

Martin Lorenz

Abstract. We give a description of the kernel of the
induction map $K_0(R) \rightarrow K_0(S)$, where $S$
is a commutative ring and $R=S^G$ is the ring of invariants
of the action of a finite group $G$ on $S$. The description
is in terms of $H^1(G,{\rm GL}(S))$.