  We launch a systematic search for phenomenologically appealing string vacua
with intersecting D-branes on the promising T6/Z(2)xZ(6)xOR orientifold with
discrete torsion. The number of independent background lattices is reduced from
six to two by new symmetries. The occurrence of USp(2N) and SO(2N) versus U(N)
gauge groups is classified as well as D-branes without matter in the adjoint
and/or symmetric representation. Supersymmetric fractional D6-branes allowing
for RR tadpole cancellation are fully classified in terms of all possible
values of the one complex structure modulus inherited from the underlying
six-torus. We then systematically investigate the conditions for three particle
generations at pairwise intersections of two D6-branes. Global SU(5) GUT models
on T6/Z(2)xZ(6)xOR are excluded by demanding three generations and no exotic
matter in the 15 representation. Two prototypes of global Pati-Salam models
with a mild amount of vector-like exotic matter are found.
