La K-Théorie de la C*-Algèbre Pleine de SL3(C)

Let G be SL3(C), λ : C*(G)→Cr*(G) the morphism induced by the regular representation, and ε : C*(G)→ C the trivial representation. We prove that λ⊕ε induces a KK-equivalence between C*(G) and Cr*(G)⊕ C. We prove this by comparing C*(G) with C(G/P)⋊G where P is a maximal parabolic subgroup in G. As a corollary, we obtain the computation of K*(C*(G)).