  We use filtrations of the tangent bundle of a manifold starting with an
integrable subbundle to define transverse symbols to the corresponding
foliation, define a condition of transversally Rockland and prove that
transversally Rockland operators yield a K-homology class. We construct an
equivariant KK-class for transversally Rockland transverse symbols and show a
Poincare duality type result linking the class of an operator and its symbol.
