  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 DGLA's. This
motivates a definition of quantum action in terms of $L_\infty$-morphisms which
generalizes the one given by Drinfeld.
