  The gauge structure of the four dimensional effective theory (4DET) arising
from a pure Yang-Mills theory in five dimensions compactified on the orbifold
$S^1/Z_2$ is reexamined on the basis of the BRST symmetry. The two scenarios
that can arise are analyzed: if the gauge parameters propagate in the bulk, the
excited Kaluza-Klein (KK) modes are gauge fields, but they are matter vector
fields if these parameters are confined in the 3-brane. In the former case, it
is shown that the 4DET is gauge invariant only if the compactification is
carried out by using curvatures instead of gauge fields as fundamental objects.
It is shown that the 4DET is governed by two types of gauge transformations,
one determined by the KK zero modes of the gauge parameters and the other by
the excited KK modes. The Dirac's method and the proper solution of the master
equation are employed to show that the theory is subject to first class
constraints. A gauge-fixing procedure to quantize the KK modes, that is
covariant under the first type of gauge transformations, is introduced. The
ghost sector induced by these gauge-fixing functions is derived on the basis of
the BRST formalism. The effective quantum Lagrangian that links the
interactions between light physics and heavy physics is presented. Concerning
the radiative corrections of the excited KK modes on the light Green functions,
the predictive character of this Lagrangian is stressed. In the case of the
gauge parameters confined to the 3-brane, the known result in the literature is
reproduced with some minor variants, although it is emphasized that the excited
KK modes are not gauge fields, but matter fields that transform under the
adjoint representation of $SU_4(N)$. The Dirac's method is employed to show
that this theory is subject to both first and second class constraints.
