  We obtain a U(M) action for supermembranes with central charges in the Light
Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of
the supermembrane together with the invariance under a U(M) gauge group with M
arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it
corresponds to M parallel supermembranes minimally immersed on the target M9xT2
(MIM2). In order to ensure the invariance under the symmetries and to close the
corresponding algebra, a star-product determined by the central charge
condition is introduced. It is constructed with a nonconstant symplectic
two-form where curvature terms are also present. The theory is in the strongly
coupled gauge-gravity regime. At low energies, the theory enters in a
decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for
any number of M2-branes. We analyze also other limits of the theory: when M
goes to we obtain a condensate of M2-branes. If we consider, instead of the
exact action, its matrix regularized version, for suitable large N but with a
finite number of colors, the algebra of the first class-constraints also closes
with the ordinary product and we obtain a regularized 2+1D SU(M) SYM theory in
the IR phase that is coupled to the SU(N) regularized supermembrane action. The
supersymmetric regularized theory with the ordinary product has purely discrete
spectrum. Our theory with the star-product is a full-fledged description of
multiple M2-branes minimally immersed in distinction with other constructions
that represent multiple M2-branes in the low energy approximation.
