Equivariant operads, string topology, and Tate cohomology

From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this theory to the little disk operad C (which is an S ¹-operad) we obtain variations on Getzler's gravity operad, which we show governs the Chas-Sullivan string bracket.