Identification of Berezin-Toeplitz Deformation Quantization

We give a complete identification of the deformation quantization which was obtained from the Berezin- Toeplitz quantization on an arbitrary compact Kähler manifold. The deformation quantization with the opposite star-product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated. Its characteristic dass (which dassifies star-products up to equivalence) is obtained. The proof is based on the microlocal description of the Szegö kernel of a strictly pseudoconvex domain given by Boutet de Monvel and Sjöstrand