  It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori
arise naturally in consideration of toroidal compactifications of M(atrix)
theory. A similar analysis of toroidal Z_{2} orbifolds leads to the algebra
B_{\theta} that can be defined as a crossed product of noncommutative torus and
the group Z_{2}. Our paper is devoted to the study of projective modules over
B_{\theta} (Z_{2}-equivariant projective modules over a noncommutative torus).
We analyze the Morita equivalence (duality) for B_{\theta} algebras working out
the two-dimensional case in detail.
