Some recent papers

Index, eta and rho invariants on foliated bundles. (with P. Piazza)  Astérisque 327 (2009), 199-284. Abstract:We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator on the maximal Connes-Skandalis Hilbert module and explain how its functional calculus encodes both the leafwise calculus and the monodromy calculus in the corresponding von Neumann algebras. When the foliation is endowed with a holonomy invariant transverse measure, we explain the compatibility of various traces and determinants. We extend Atiyah's index theorem on Galois coverings to these foliations. We define a foliated rho-invariant and investigate its stability properties for the signature operator. Finally, we establish the foliated homotopy invariance of such a signature rho-invariant under a Baum-Connes assumption, thus extending to the foliated context results proved by Neumann, Mathai, Weinberger and Keswani on Galois coverings.
The higher fixed point theorem for foliations. I Holonomy invariant currents (with J. Heitsch)  J. of Funct. Analysis 259, (2010), 131-173. Abstract: We prove a higher fixed point formula for foliations in the presence of a closed Haefilger current.To this end we associate with such current an equivariant cyclic cohomology class of Connes' C* algebra of the foliation, and compute its pairing with the localized equivariant K-theory in terms of local contributions near the fixed points.
Homotopy invariance of the higher harmonic signature. (with J. Heitsch) To appear in J. of Diff. Geometry. Abstract: We define the higher harmonic signature, twisted by a leafwise U(p,q)-flat bundle, of an even dimensional oriented Riemannian foliation of a compact Riemannian manifold, and prove that it is a leafwise homotopy invariant. In the process, we also prove that the projection onto the leafwise harmonic forms in the middle dimension for the associated foliation of the graph is transversely smooth in the definite case. Some consequences for the Novikov conjecture are also investigated.
On the analyticity of the bivariant JLO cocycle. (with A. Carey) Submitted Abstract: We prove that for any smooth fibration of closed manifolds, there is a well defined bivariant JLO cocycle which turns out to be analytic in the sense of Ralf Meyer's theory.
Local index theorem for projective families. (with A. Gorokhovsky) Submitted Abstract: We give a superconnection proof of the Mathai-Melrose-Singer index theorem for the family of twisted Dirac operators.