Existence and K-theory conjecture for projective quantization dg-modules

Let $M$ be a symplectic manifold, let ${\cal W}$ be its Weyl algebra bundle, and let $(\Omega(M, {\cal W}), \nabla, R)$ be the associated $Q$-algebra. A finitely generated projective quantization dg-module is a finitely generated projective module over this $Q$-algebra equipped with the stated quantization dg-structure. Existence and K-theory conjecture. The $Q$-algebra $(\Omega(M, {\cal W}), \nabla, R)$ has finitely generated projective quantization dg-modules. Furthermore, the $K$-group of finitely generated projective quantization dg-modules over $(\Omega(M, {\cal W}), \nabla, R)$ is isomorphic to the $K$-group of finitely generated projective modules over $C^\infty(M)$. The conjecture extends the affirmative construction given in the source for a two-dimensional torus with constant Poisson structure to general symplectic manifolds, while the corresponding existence question is explicitly stated as unknown there.