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Let M be a foliated manifold and G a discrete group acting on M bydiffeomorphisms mapping leaves to leaves. Then G naturally acts byautomorphisms on the algebra of Heisenberg pseudodifferential operators on thefoliation. Our main result is an index theorem for hypoelliptic-type operatorswhich belong to the crossed product of the Heisenberg pseudodifferentialoperators with the group G. As a corollary, we get a solution toConnes-Moscovici's transverse problem in arbitrary codimensions, by exhibitingan explicit formula in terms of characteristic classes of equivariant vectorbundles over M, for the Chern-Connes character associated to their hypoellipticsignature operator.

An equivariant index theorem for hypoelliptic operators