In this paper we provide a quantization via formality of Poisson actions of a triangular Lie algebra $(mathfrak g,r)$ on a smooth manifold $M$. Using the formality of polydifferential operators on Lie algebroids we obtain a deformation quantization of $M$ together with a quantum group $mathscr{U}_hbar(mathfrak{g})$ and a map of associated DGLAs. This motivates a definition of quantum action in terms of $L_infty$-morphisms which generalizes the one given by Drinfeld.
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