Type IIA orientifolds and orbifolds on non-factorizable tori

We investigate type II orientifolds on non-factorizable torus with and without its oribifolding. We explicitly calculate the Ramond-Ramond tadpole from string one-loop amplitudes, and confirm that the consistent number of orientifold planes is directly derived from the Lefschetz fixed point theorem. We furthermore classify orientifolds on non-factorizable ZN×ZM orbifolds, and construct new supersymmetric type IIA orientifold models on them.