ar X iv : 0 70 8 . 42 79 v 2 [ m at h . K T ] 2 9 M ay 2 00 8 A LEFSCHETZ FIXED - POINT FORMULA FOR CERTAIN ORBIFOLD C * - ALGEBRAS
نویسنده
چکیده
Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product C-algebras C0(X)⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊ G induced by the endomorphism, i.e. the Lefschetz number, in terms of fixed orbits and representation-theoretic data connected with certain isotropy subgroups of the isotropy group at that point.
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