B_s^0-\bar{B}_s^0 mixing and B -> \pi K decays in stringy leptophobic Z^\prime

We consider a leptophobic Z^\prime scenario in a flipped SU(5) grand unified theory obtained from heterotic string theory. We show that the allowed Z^\prime mass, flavor conserving and flavor changing couplings of the Z^\prime to the down-type quarks are strongly constrained by the mass difference in B_s-\bar{B}_s system and the four branching ratios of B -> \pi K decays. It is shown that even under these constraints large deviations in direct and/or indirect CP asymmetries of B \to \pi K decays from the SM expectations are allowed. Especially it is possible to accommodate the apparent puzzling data in B -> \pi K CP asymmetries.