  We investigate a nonlocal chiral quark model with separable 4-fermion
interaction for the case of U(3) flavor symmetry and show that strange quark
matter is unlikely to occur in a large enough volume of a compact star to
entail remarkable observational consequences. The phase diagram in the
two-flavor sector of such model has a critical end point of the line of first
order chiral/deconfinement phase transitions on which a triple point marks the
junction with the critical line for second order phase transitions to
two-flavor color superconductivity (2SC) below T~80 MeV. Stable hybrid star
configurations with large quark matter core in a color superconducting phase
can exist. A consistent cooling phenomenology requires that all quark species
be gapped, the minimal pairing gap of the order of 10 - 100 keV.
