We report on our on-going joint work with B. Rangipour on realizing the characteristic classes of symplectic foliations of codimension 2 in the cyclic cohomology of the groupoid action algebra.

Using a cup product construction, one can construct a characteristic homomorphism from the truncated Weil algebra of the general linear Lie algebra gl(n) to the groupoid action algebra upon which the Connes-Moscovici Hopf algebra H_n acts.

By this characteristic homomorphism, we transfer the characteristic classes of (smooth) foliations of codimension 1 and 2 to the cyclic cohomology of the groupoid action algebra, recovering the results of Connes and Moscovici in codimension 1.

One then expects to carry out a similar construction, with the symplectic Hopf-algebra SpH_n, to transfer the characteristic classes of symplectic foliations. In this talk, we briefly disscuss the challenges/problems we have encountered in this symplectic case.