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 θ 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 θ (Z 2 -equivariant projective modules over a noncommutative torus). We analyze the Morita equivalence (duality) for B θ algebras working out the two-dimensional case in detail.