A Lefschetz fixed-point formula for certain orbifold -algebras

  • Siegfried Echterhoff

    Unversity of Münster, Germany
  • Heath Emerson

    University of Victoria, Canada
  • Hyun Jeong Kim

    University of Victoria, Canada


Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product -algebras coming from covariant pairs. Here is assumed countable, a manifold, and cocompact and proper. The formula in question describes the graded trace of the map induced by the automorphism on K-theory of , 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.

Cite this article

Siegfried Echterhoff, Heath Emerson, Hyun Jeong Kim, A Lefschetz fixed-point formula for certain orbifold -algebras. J. Noncommut. Geom. 4 (2010), no. 1, pp. 125–155

DOI 10.4171/JNCG/51