  We show that the $D=11$ Supermembrane theory (M2-brane) compactified on a
$M_9 \times T^2$ target space, with constant fluxes $C_{\pm}$ naturally
incorporates the geometrical structure of a twisted torus. We extend the
M2-brane theory to a formulation on a twisted torus bundle. It is consistently
fibered over the world volume of the M2-brane. It can also be interpreted as a
torus bundle with a nontrivial $U(1)$ connection associated to the fluxes. The
structure group $G$ is the area preserving diffeomorphisms. The torus bundle is
defined in terms of the monodromy associated to the isotopy classes of
symplectomorphisms with $\pi_{0} (G) = SL(2,Z)$, and classified by the
coinvariants of the subgroups of $SL(2,Z)$. The spectrum of the theory is
purely discrete since the constant flux induces a central charge on the
supersymmetric algebra and a modification on the Hamiltonian which renders the
spectrum discrete with finite multiplicity. The theory is invariant under
symplectomorphisms connected and non connected to the identity, a result
relevant to guaranteed the U-dual invariance of the theory. The Hamiltonian of
the theory exhibits interesting new $U(1)$ gauge and global symmetries on the
worldvolume induced by the symplectomorphim transformations. We construct
explicitly the supersymmetric algebra with nontrivial central charges. We show
that the zero modes decouple from the nonzero ones. The nonzero mode algebra
corresponds to a massive superalgebra that preserves either $1/2$ or $1/4$ of
the original supersymmetry depending on the state considered.
