Formality theorem for g-manifolds

With any g-manifold M are associated two dglas tot(Λ^•g^∨⊗_kT_poly^•(M)) and tot(Λ^•g^∨⊗_kD_poly^•(M)), whose cohomologies H_CE^•(g,T_poly^•(M)→0T_poly^•+1(M)) and H_CE^•(g,D_poly^•(M)→d_HD_poly^•+1(M)) are Gerstenhaber algebras. We establish a formality theorem for g-manifolds: there exists an L_∞ quasi-isomorphism Φ:tot(Λ^•g^∨⊗_kT_poly^•(M))→tot(Λ^•g^∨⊗_kD_poly^•(M)) whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the g-manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the g-manifold M is an isomorphism of Gerstenhaber algebras from H_CE^•(g,T_poly^•(M)→0T_poly^•+1(M)) to H_CE^•(g,D_poly^•(M)→d_HD_poly^•+1(M)).