On the global construction of modules over Fedosov deformation quantization algebra

Let $(M,\omega )$ be a symplectic manifold, $\mathcal{D}\subset TM$ a real polarization on $M$ and $\mathrm{\wp }$ a leaf of $\mathcal{D}$. We construct a Fedosov-type star-product ${\ast }_L$ on $M$ such that $C^{\mathrm{\infty }}(\mathrm{\wp })[[h]]$ has a natural structure of left module over the deformed algebra $(C^\infty (M)[[h]], \ast_L)$. This generalizes the results of 0708.2626.