On the twisted KK-homology of simple Lie groups

We prove that the twisted KK-homology of a simply connected simple Lie group GG of rank nn is an exterior algebra on n−1n−1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of GG and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted Spinc bordism group of GG.