  We study an Abelian compact gauge theory minimally coupled to bosonic matter
with charge q, which may undergo a confinement--deconfinement transition in
(2+1)D. The transition is analyzed using a nonlocal order parameter $\tilde W$,
which is related to large Wilson loops for fractional charges. We map the model
to a dual representation with no gauge field but only a global q-state clock
symmetry and show that $\tilde W$ correspond to the domain wall energy of that
model. $\tilde W$ is also directly connected to the concept of topological
order. We exploit these facts in Monte Carlo simulations to study the detailed
nature of the deconfinement transition.
