  Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic
symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of
the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of
codimension $q$ and a vector bundle $E$ on $Y$. We show that if $j_* E$ admits
a deformation quantization (as a module) then its characteristic class
$\widehat{A}(M) exp(-c(\mathcal{O}_h)) ch(j_* E)$ lifts to a cohomology group
associated to the null foliation of $Y$. Moreover, it can only be nonzero in
degrees $2q, \ldots, 2(p+q)$. For Lagrangian $Y$ this reduces to a single
degree $2q$. Similar results hold in the holomorphic category.
  This is a companion paper of a joint work with Victor Ginzburg on general
quantizable sheaves.
