Deformation quantization on cotangent bundles

In this note we construct natural star-products on cotangent bundles of Riemannian manifolds. Hereby we essentially use a parameter dependent symbol calculus for pseudo-differential operators on manifolds. The constructed star-products generalize the well-known λ-ordered quantization scheme on R2n. In particular we thus extend Weyl quantization but also normal and antinormal order quantization to cotangent bundles of Riemannian manifolds.