  Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$,
$\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of
$\omega_0$. We prove that for a complex polarization of $\omega$ there exists a
commutative subalgebra, $O$, in $A$ that is isomorphic to the algebra of
functions constant along the polarization.
  Let $F(A)$ consists of elements of $A$ whose commutator with $O$ belongs to
$O$. Then, $F(A)$ is a Lie algebra which is an $O$-extension of the Lie algebra
of derivations of $O$. We prove a formula which relates the class of this
extension, the Fedosov class, and the Chern class of $P$.
