A Lefschetz fixed-point formula for certain orbifold C*-algebras

Echterhoff, Siegfried; Emerson, Heath; Kim, Hyun Jeong

A Lefschetz fixed-point formula for certain orbifold C*-algebras

Authors

Echterhoff, Siegfried

Emerson, Heath

Kim, Hyun Jeong

Description

Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C*-algebras $C_0(X)\cross G$ coming from covariant pairs. Here $G$ is assumed countable, $X$ a manifold, and $X\cross G$ cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of $C_0(X)\cross G$ induced by the endomorphism, \emph{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. The technique is to use noncommutative Poincaé duality and the formal Lefschetz lemma of the second author.
26 pages