  We study the Hochschild homology groups of the algebra of complete symbols on
a foliated manifold $(M,F)$. The first step is to relate these groups to the
Poisson homology of $(M,F)$ and of other related foliated manifolds. We then
establish several general properties of the Poisson homology groups of foliated
manifolds. As an example, we completely determine these Hochschild homology
groups for the algebra of complete symbols on the irrational slope foliation of
a torus (under some diophantine approximation assumptions). We also use our
calculations to determine all residue traces on algebras of pseudodifferential
operators along the leaves of a foliation.
