  We construct a Z_2 orbifold projection of SU(N) gauge theories formulated in
five dimensions with a compact fifth dimension. We show through a
non-perturbative argument that no boundary mass term for the Higgs field,
identified with some of the fifth dimensional components of the gauge field, is
generated, which would be quadratically divergent in the five-dimensional
ultraviolet cutoff. This opens the possibility of studying these theories
non-perturbatively in order to establish if they can be used as effective
weakly interacting theories at low energies. We make preparations for a study
on the lattice. In particular we show that only Dirichlet boundary conditions
are needed, which specify the breaking pattern of the gauge group at the
orbifold fixpoints.
