  The moduli space of the maximally supersymmetric heterotic string in
d-dimensional Minkowski space contains various components characterized by the
rank of the gauge symmetries of the vacua they parametrize. We develop an
approach for describing in a unified way continuous Wilson lines which
parametrize a component of the moduli space, together with discrete
deformations responsible for the switch from one component to the other.
Applied to a component that contains vacua with SO(2n+1) gauge-symmetry
factors, our approach yields a description of all backgrounds of the component
in terms of free-orbifold models. The orbifold generators turn out to act
symmetrically or asymmetrically on the internal space, with or without discrete
torsion. Our derivations use extensively affine characters of SO(2n+1). As a
by-product, we find a peculiar orbifold description of the heterotic string in
ten dimensions, where all gauge degrees of freedom arise as twisted states,
while the untwisted sector reduces to the gravitational degrees of freedom.
