TWISTED EQUIVARIANT K-THEORY WITH COMPLEX COEFFICIENTS

DANIEL FREED MICHAEL HOPKINS CONSTANTIN TELEMAN

Abstract. Using a global version of the equivariant Chern character supported over the entire group, we describe an effective method for computing the complexified twisted equivariant K-theory of a space with compact Lie group action, in terms of fixed-point data. We apply this to the case of a Ad-action of the group on itself, and relate the result top the Verlinde algebra and the Kac character formula of the loop group. The Verlinde formula for the dimensions of the spaces of conformal blocks is also discussed in the same context.