  We construct heterotic string backgrounds corresponding to families of
homogeneous spaces as exact conformal field theories. They contain left cosets
of compact groups by their maximal tori supported by NS-NS 2-forms and gauge
field fluxes. We give the general formalism and modular-invariant partition
functions, then we consider some examples such as SU(2)/U(1) ~ S^2 (already
described in a previous paper) and the SU(3)/U(1)^2 flag space. As an
application we construct new supersymmetric string vacua with magnetic fluxes
and a linear dilaton.
