Polyvector fields and polydifferential operators associated with Lie pairs

We prove that the spaces tot (Γ(λ•A)⊗Rt•polly;) and tot (Γ(λ•A)⊗RD•polly;) associated with a Lie pair (L,A) each carry an L∞algebra structure canonical up to an L1 isomorphism with the identity map as linear part. These two spaces serve, respectively, as replacements for the spaces of formal polyvector fields and formal polydifferential operators on the Lie pair (L,A). Consequently, both H•CE(A t•polly;) and H•CE(A D•polly;) admit unique Gerstenhaber algebra structures. Our approach is based on homotopy transfer and the construction of a Fedosov dg Lie algebroid (i.e. a dg foliation on a Fedosov dg manifold)