  Let G be a connected reductive algebraic group acting on a scheme X. Let R(G)
denote the representation ring of G, and let I be the ideal in R(G) of virtual
representations of rank 0. Let G(X) (resp. G(G,X)) denote the Grothendieck
group of coherent sheaves (resp. G-equivariant coherent sheaves) on X.
Merkurjev proved that if the fundamental group of G is torsion-free, then the
map of G(G,X)/IG(G,X) to G(X) is an isomorphism. Although this map need not be
an isomorphism if the fundamental group of G has torsion, we prove that without
the assumption on the fundamental group of G, this map is an isomorphism after
tensoring with the rational numbers.
