  The heterotic $E_8\times E_8$ string compactified on an orbifold $T^4/\IZ_N$
has gauge group $G\times G'$ with (massless) states in its twisted sectors
which are charged under both gauge group factors. In the dual M-theory on
$(T^4/\IZ_N)\otimes(S^1/\IZ_2)$ the two group factors are separated in the
eleventh direction and the G and G' gauge fields are confined to the two
boundary planes, respectively. We present a scenario which allows for a
resolution of this apparent paradox and assigns all massless matter multiplets
locally to the different six-dimensional boundary fixed planes. The resolution
consists of diagonal mixing between the gauge groups which live on the
connecting seven-planes (6d and the eleventh dimension) and one of the gauge
group factors. We present evidence supporting this mixing by considering gauge
couplings and verify local anomaly cancellation. We also discuss open problems
which arise in the presence of U_1 factors.
