The anticyclic operad of moulds

A new anticyclic operad Mould is introduced, on spaces of functions in several variables. It is proved that the Dendriform operad is an anticyclic suboperad of this operad. Many operations on the free Mould algebra on one generator are introduced and studied. Under some restrictions, a forgetful map from moulds to formal vector fields is then defined. A connection to the theory of tilting modules for quivers of type A is also described.