We consider the effect of the (heavy) fundamental quarks on the low energy
effective Lagrangian description of non-Abelian gauge theories in 2+1 dimen
sions. We show that in the presence of the fundamental charges, the magneti
c Z(N) symmetry becomes local. We construct the effective Lagrangian repres
enting this local symmetry in terms of magnetic vortex fields, and discuss
its physical consequences. We show that the finite energy states described
by this Lagrangian have distinct bag-like structure. The point-like quarks
are confined to the region of space where the value of the vortex field is
much smaller than in the surrounding vacuum.