  We present the construction of exactly solvable superconformal field theories
describing Type II string models compactified on compact G_2 manifolds. These
models are defined by anti-holomorphic quotients of the form (CY*S^1)/Z_2,
where we realize the Calabi-Yau as a Gepner model. In the superconformal field
theory the Z_2 acts as charge conjugation implying that the representation
theory of a W(2,4,6,8,10) algebra plays an important role in the construction
of these models. Intriguingly, in all three examples we study, including the
quintic, the massless spectrum in the Z_2 twisted sector of the superconformal
field theory differs from what one expects from the supergravity computation.
This discrepancy is explained by the presence of a discrete NS-NS background
two-form flux in the Gepner model.
