  In this article, $X$ will denote a ${\cal C}^{\infty}$ manifold. In a very
famous article, Kontsevich showed that the differential graded Lie algebra
(DGLA) of polydifferential operators on $X$ is formal. Calaque extended this
theorem to any Lie algebroid. More precisely, given any Lie algebroid $E$ over
$X$, he defined the DGLA of $E$-polydifferential operators, $\Gamma (X,
^{E}D^{*}_{poly})$, and showed that it is formal. Denote by $\Gamma (X,
^{E}T^{*}_{poly})$ the DGLA of $E$-polyvector fields. Considering $M$, a module
over $E$, we define $\Gamma (X, ^{E}T_{poly}^{*}(M))$ the $\Gamma (X,
^{E}T^{*}_{poly})$-module of $E$-polyvector fields with values in $M$.
Similarly, we define the $\Gamma (X, ^{E}D^{*}_{poly})$-module of
$E$-polydifferential operators with values in $M$, $\Gamma (X,
^{E}D^{*}_{poly}(M))$. We show that there is a quasi-isomorphism of
$L_{\infty}$-modules over $\Gamma (X, ^{E}T^{*}_{poly})$ from $\Gamma (X,
^{E}T^{*}_{poly}(M))$ to $\Gamma (X, ^{E}D^{*}_{poly}(M))$. Our result extends
Calaque 's (and Kontsevich's) result.
