Noncommutative Chern Characters of Compact Lie Group C*-Algebras

For compact Lie groups, the Chern characters K^*(G) Q H^*_DR(G;Q) have been already constructed. In this paper, we construct and study the corresponding noncommutative Chern characters. They are homomorphisms ch_C*: K_*(C^*(G)) from quantum K-groups into entire current periodic cyclic homology groups of group C^*-algebras. We also obtain the corresponding algebraic version ch_alg: K_*(C^*(G)) HP_*(C^*(G)), which can be identified with the classical Chern character K_* (C(T)) HP_* (C(T)), where T is the maximal torus of G.