  We discuss toroidal orbifolds of the E8XE8 heterotic string, in which the
free fermionic Higgs-matter splitting is implemented by a shift in the internal
lattice coupled with the fermion numbers of the gauge degrees of freedom. We
consider models in which some choices of the orbifold result in the projection
of the graviton. In the models that we consider the projection also results in
flipping the spin-statistics assignments in the massive string spectrum,
whereas the massless spectrum retains the conventional spin-statistics
assignments. We argue that the partition functions are mathematically
consistent for one- and multi-loop amplitudes, owning to the existence of
supersymmetry in the spectrum. A duality between different models at nonzero
temperature is briefly discussed.
