Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras, by Victor Nistor

We give a detailed calculation of the Hochschild and cyclic homology of the algebra CIc(G) of locally constant, compactly supported functions on a reductive p-adic group G. We use these calculations to extend to arbitrary elements the definition the higher orbital integrals introduced by Blanc and Brylinski for regular semisimple elements. Then we extend to higher orbital integrals some results of Shalika. We also investigate the effect of the ``induction morphism'' on Hochschild homology.

Victor Nistor <nistor@math.psu.edu>