  In this paper we study the category of standard holomorphic vector bundles on
a noncommutative two-torus. We construct a functor from the derived category of
such bundles to the derived category of coherent sheaves on an elliptic curve
and prove that it induces an equivalence with the subcategory of stable
objects. By the homological mirror symmetry for elliptic curves this implies an
equivalence between the derived category of holomorphic bundles on a
noncommutative two-torus and the Fukaya category of the corresponding
symplectic (commutative) torus.
