Weinstein's conjecture on tangential star products for Lie algebra duals

Let $\mathfrak{g}$ be a Lie algebra with corresponding Lie group $G$. A tangential star product on the dual $\mathfrak{g}^*$ is a star product compatible with the symplectic-leaf decomposition into coadjoint orbits. The cotangent bundle $T^*G$ has a decomposition into the left (or right) translates of coadjoint orbits.

Weinstein's conjecture. The dual $\mathfrak{g}^*$ admits a tangential star product if and only if there is a flat torsion-free affine connection on a neighborhood of the identity in $G$ for which the induced connection on the vector bundle $T^*G$ is compatible with the decomposition into the left (or right) translates of coadjoint orbits.

This conjecture relates tangential deformation quantization of the linear Poisson structure on a Lie algebra dual to affine-geometric structure on the corresponding Lie group. The supplied text does not state whether the conjecture is resolved.