  We consider pure SU(N) gauge theories defined on an orbifold lattice,
analogous to the S^1/Z_2 gauge theory orbifolds of the continuum, which
according to the perturbative analysis do not have a Higgs phase.
Non-perturbatively the conclusion for N even is the opposite, namely that
spontaneous symmetry breaking does take place and some of the gauge bosons
become massive. We interpret this new, non-perturbative phenomenon both
mathematically and physically.
