  We have computed one-loop bulk and brane mass renormalization effects in a
five-dimensional gauge theory compactified on the M_4 \times S^1/Z_2 orbifold,
where an arbitrary gauge group G is broken by the orbifold action to its
subgroup H. The space-time components of the gauge boson zero modes along the H
generators span the gauge theory on the orbifold fixed point branes while the
zero modes of the higher-dimensional components of the gauge bosons along the
G/H generators play the role of Higgs fields with respect to the gauge group H.
No quadratic divergences in the mass renormalization of the gauge and Higgs
fields are found either in the bulk or on the branes. All brane effects for the
Higgs field masses vanish (only wave function renormalization effects survive)
while bulk effects are finite and can trigger, depending on the fermionic
content of the theory, spontaneous Hosotani breaking of the brane gauge group
H. For the gauge fields we do find logarithmic divergences corresponding to
mass renormalization of their heavy Kaluza-Klein modes. Two-loop brane effects
for Higgs field masses are expected from wave function renormalization brane
effects inserted into finite bulk mass corrections.
