  We show that the Connes-Moscovici cyclic cohomology of a Hopf algebra
equipped with a character has a Lie bracket of degree -2. More generally, we
show that a "cyclic operad with multiplication" is a cocyclic module whose
cohomology is a Batalin-Vilkovisky algebra and whose cyclic cohomology is a
graded Lie algebra of degree -2. This explain why the Hochschild cohomology
algebra of a symmetric algebra is a Batalin-Vilkovisky algebra.
