  The dual of an arbitrary $D$-dimensional nonabelian lattice gauge theory,
obtained after character expansion and integration over the gauge group, is
shown to be a {\em local} lattice theory in the eigenspace of the Casimir
operators. For $D\leq4$ we also provide the explicit form of the action as a
product of character expansion coefficients and Racah coefficients. The
representation can be used to facilitate strong coupling expansions.
Furthermore, the possibility of simulations, at weak coupling, in the dual
representation, is also discussed.
