Title: APS index theorem for proper action of Lie groups
Abstract: Given a proper, cocompact action of a connected, linear real reductive group, we define a delocalized eta-invariants of invariant Dirac operators. We then explain how these invariants enter as boundary correction terms in a APS-type index theorem. For pure Dirac operators this works under an L2-invertibility assumption of the boundary operator, and we also discuss different types of perturbations of Dirac operators to remove this assumption. This talk is based on joint work with Paolo Piazza, Hessel Posthuma, and Xiang Tang.