Quantum SU(2) and the Baum-Connes conjecture

We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group $ SU_q(2) $ of Woronowicz. As an illustration of this result we determine the $ K $-groups of quantum automorphism groups of simple matrix algebras.
Comment: 14 pages, contribution to the Proceedings of the Conference in Honour of the seventieth birthday of S. L. Woronowicz