  We reduce M-theory on a G_2 orbifold with co-dimension four singularities,
taking explicitly into account the additional gauge fields at the
singularities. As a starting point, we use 11-dimensional supergravity coupled
to seven-dimensional super-Yang-Mills theory, as derived in a previous paper.
The resulting four-dimensional theory has N=1 supersymmetry with non-Abelian
N=4 gauge theory sub-sectors. We present explicit formulae for the Kahler
potential, gauge-kinetic function and superpotential. In the four-dimensional
theory, blowing-up of the orbifold is described by a Higgs effect induced by
continuation along D-flat directions. Using this interpretation, we show that
our results are consistent with the corresponding ones obtained for smooth G_2
spaces. In addition, we consider the effects of switching on flux and Wilson
lines on singular loci of the G_2 space, and we discuss the relation to N=4 SYM
theory.
