Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels

Bound states generated by the K coupled PT-symmetric square wells are studied in a series of models where the Hamiltonians are assumed R-pseudo-Hermitian and R-2-symmetric. Specific rotation-like generalized parities R are considered such that R-N = I at some integers N. We show how our assumptions make the models exactly solvable and quasi-Hermitian. This means that they possess the real spectra as well as the standard probabilistic interpretation.