Let be a finite group acting on a compact manifold and let denote the algebra of classical complete symbols on . We determine all traces on the cross-product algebra as residues of certain meromorphic zeta functions. Further we compute the cyclic homology for in terms of the de Rham cohomology of the fixed point manifolds . In the process certain new results on the homologies of general cross-product algebras are obtained.
Cite this article
Shantanu Dave, An equivariant noncommutative residue. J. Noncommut. Geom. 7 (2013), no. 3, pp. 709–735DOI 10.4171/JNCG/132