  The Zirnbauer's color-flavor transformation is applied to the $U(N_c)$
lattice gauge model, in which the gauge theory is induced by a heavy chiral
scalar field sitting on lattice sites. The flavor degrees of freedom can
encompass several `generations' of the auxiliary field, and for each
generation, remaining indices are associated with the elementary plaquettes
touching the lattice site. The effective, color-flavor transformed theory is
expressed in terms of gauge singlet matrix fields carried by lattice links. The
effective action is analyzed for a hypercubic lattice in arbitrary dimension.
We investigate the corresponding d=2 and d=3 dual lattices. The saddle points
equations of the model in the large-$N_c$ limit are discussed.
