Supersymmetric ZN×ZM orientifolds in 4D with D-branes at angles

We construct orientifolds of type IIA string theory. The theory is compactified on a T6/ZN×ZM orbifold. In addition worldsheet parity in combination with a reflection of three compact directions is modded out. Tadpole cancellation requires to add D-6-branes at angles. The resulting four dimensional theories are N=1 supersymmetric and non-chiral.