  Consider on a manifold the solution $X$ of a stochastic differential equation
driven by a L\'evy process without Brownian part. Sufficient conditions for the
smoothness of the law of $X_t$ are given, with particular emphasis on
noncompact manifolds. The result is deduced from the case of affine spaces by
means of a localisation technique. The particular cases of Lie groups and
homogeneous spaces are discussed.
