Genuine equivariant operads

Abstract We build new algebraic structures, which we call genuine equivariant operads and which can be thought of as a hybrid between operads and coefficient systems. We then prove an Elmendorf-Piacenza type theorem stating that equivariant operads, with their graph model structure, are equivalent to genuine equivariant operads, with their projective model structure. As an application, we build explicit models for the N ∞ -operads of Blumberg and Hill.