Deformation quantization for almost-Kahler manifolds

On an arbitrary almost-Kahler manifold, starting from a natural affine connection with nontrivial torsion which respects the almost-Kahler structure, in joint work with A. Karabegov a Fedosov-type deformation quantization on this manifold was constructed. This contribution reports on the result and supplies an overview of the essential steps in the construction. On this way Fedosov's geometric method is explained.