  Consider a spin manifold M, equipped with a line bundle L and an action of a
compact Lie group G. We can attach to this data a family Theta(k) of
distributions on the dual of the Lie algebra of G. The aim of this paper is to
study the asymptotic behaviour of Theta(k) when k is large, and M possibly non
compact, and to explore a functorial consequence of this formula for reduced
spaces.
