  For a reductive group scheme over a regular semi-local ring, we prove an
equivarinat version of the Gersten conjecture. We draw some interesting
consequences for the representation rings of such reductive group schemes. We
also prove the rigidity for the equivariant K-theory of reductive group schemes
over a henselian local ring. This is then used to compute the equivariant
K-theory of algebraically closed fields.
