  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 in
\cite{Blanc-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.
