Hypoelliptic Laplacian and orbital integrals (Q1032851)

The author gives a new method to compute semi-simple orbital integrals based on the theory of hypoelliptic Laplacian. This theory furnishes a family of hypoelliptic operators in the total space of the tangent or cotangent bundle of a Riemannian manifold related in a certain way to the usual Hodge theory and to the geodesic flow. The formalism unifies the Atiyah-Singer index theorem and the trace formula.