For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.
Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group
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abstract
Recall that Tamarkin's construction arXiv:math/9803025, arXiv:math/0003052 gives us a map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains of a polynomial algebra. Due to results of V. Drinfeld (Algebra i Analiz 2, (1990)) and T. Willwacher arXiv:1009.1654 both the source and the target of this map are equipped with natural actions of the Grothendieck-Teichmueller group $GRT_1$. In this paper, we use the result from arXiv:1305.4699 to prove that this map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains is $GRT_1$-equivariant.
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M. Kontsevich's graph complexes and universal structures on graded symplectic manifolds
For every d at least 2, the full Kontsevich graph complex maps injectively into the Chevalley-Eilenberg complex of the n=d-1 Schouten algebra, so its zeroth cohomology acts via L-infinity automorphisms on graded symplectic manifolds.