On the Satake isomorphism

Abstract

In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper we give new proofs for some results of that paper, one based on the theory of J-rings and one based on the known character formula for rational representations of a reductive group in positive, large, characteristic. We also give an extension of that character formula to disconnected groups.