  The transfer of the generating operations of an algebra to a homotopy
equivalent chain complex produces higher operations. The first goal of this
paper is to describe precisely the higher structure obtained when the unary
operations commute with the contracting homotopy. To solve this problem, we
develop the Koszul duality theory of operads in the category of modules over a
cocommutative Hopf algebra. This gives rise to a simpler category of homotopy
algebras and infinity-morphisms, which allows us to get a new description of
the homotopy category of algebras over such operads. The main example of this
theory is given by Batalin-Vilkovisky algebras.
