  In 1979, M. Kashiwara and M. Vergne formulated a conjecture on a Lie group G
which implies that the Duflo isomorphism of Z(g) and S(g)^g extends to a
natural module isomorphism between the spaces of germs of invariant
distributions on G and g=Lie(G), respectively. They also proved their
conjecture for G solvable. Using Kontsevich's deformation quantization we
establish directly this result for distributions on any real Lie group G. In
turn this gives a new proof of Duflo's result on the local solvability of
bi-invariant differential operators on G.
