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)).