On the dequantization of Fedosov's deformation quantization

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of T* M to the formal neighborhood of the diagonal of the product M x (M) over tilde, where (M) over tilde is a copy of M with the opposite Poisson structure. We call it dequantization of the natural deformation quantization. Then we 'dequantize' Fedosov's quantization.