A Lefschetz fixed-point formula for certain orbifold $\mathrm C^*$-algebras
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Bibliographic record
Abstract
Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product \mathrm C^* -algebras C_0(X) ⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question describes the graded trace of the map induced by the automorphism on K-theory of C_0(X) ⋊ G , i.e. the Lefschetz number, in terms of fixed orbits of the spatial map. Each fixed orbit contributes to the Lefschetz number by a formula involving twisted conjugacy classes of the corresponding isotropy group, and a secondary construction that associates, by way of index theory, a group character to any finite group action on a Euclidean space commuting with a given invertible matrix.
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|---|---|---|
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