  Using $\star$-product on Co-adjoint orbits (K-orbits) of the $\MD_4$- groups
we obtain quantum half-planes, quantum hyperbolic cylinders, quantum hyperbolic
paraboloids...via Fedosov deformation quantization. From this we have
corresponding unitary representations of the $\MD_4$- groups. Particularly, for
groups $\G_{4,2,3(\phi)}; \G_{4,2,4}; \G_{4,3,4(\phi)}$ and $ \G_{4,4,1} $,
which are neither nilpotent nor exponential, we obtain the explicit formulas.
