  An affine vertex operator construction at arbitrary level is presented which
is based on a completely compactified chiral bosonic string whose momentum
lattice is taken to be the (Minkowskian) affine weight lattice. This
construction is manifestly physical in the sense of string theory, i.e., the
vertex operators are functions of DDF ``oscillators'' and the Lorentz
generators, both of which commute with the Virasoro constraints. We therefore
obtain explicit representations of affine highest weight modules in terms of
physical (DDF) string states. This opens new perspectives on the representation
theory of affine Kac-Moody algebras, especially in view of the simultaneous
treatment of infinitely many affine highest weight representations of arbitrary
level within a single state space as required for the study of hyperbolic
Kac-Moody algebras. A novel interpretation of the affine Weyl group as the
``dimensional null reduction'' of the corresponding hyperbolic Weyl group is
given, which follows upon re-expression of the affine Weyl translations as
Lorentz boosts.
