Abstract:According to a result of Freed-Hopkins-Teleman, the twisted equivariant K$-homology of a compact, simple, simply connected Lie group G is isomorphic to the level k fusion ring (Verlinde algebra) R_k(G). After a review of K-homology, we will show how to use this result for the `quantization' of spaces with G-valued moment maps. The elements of R_k(G) obtained in this way are then computed by localization techniques.Joint work with Anton Alekseev.