  A generalisation of discrete torsion is introduced in which different
discrete torsion phases are considered for the different fixed points or twist
fields of a twisted sector. The constraints that arise from modular invariance
are analysed carefully. As an application we show how all the different
resolutions of the T^7/Z_2^3 orbifold of Joyce have an interpretation in terms
of such generalised discrete torsion orbifolds. Furthermore, we show that these
manifolds are pairwise identified under G_2 mirror symmetry. From a conformal
field theory point of view, this mirror symmetry arises from an automorphism of
the extended chiral algebra of the G_2 compactification.
