Comparison of equivariant and ordinary K-theory of algebraic varieties, by Aleksandr S. Merkurjev

It is proved that for a reductive group G the natural homomorphism K'0(G;X) ---> K'0(X) is surjective for any quasi-projective scheme X on which G acts if and only if the Picard group of G is trivial over all finite field extensions of F. If G splits, a spectral sequence with the E2-term related to the equivariant K'-theory of X, which converges to the ordinary K'-groups of X, is constructed.

Aleksandr S. Merkurjev <>