  We introduce the new notion of convolution of a (smooth or generalized)
valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the
group. In the case of a transitive group action, we prove that the spaces of
smooth and generalized valuations on $M$ are modules over the algebra of
compactly supported generalized valuations on $G$ satisfying some technical
condition of tameness.
  The case of a vector space acting on itself is studied in detail. We prove
explicit formulas in this case and show that the new convolution is an
extension of the convolution on smooth translation invariant valuations
introduced by J.~Fu and the second named author.
