  We consider an exactly solvable model in 3+1 dimensions, based on a finite
group, which is a natural generalization of Kitaev's quantum double model. The
corresponding lattice Hamiltonian yields excitations located at
torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded
by two tori which supports states satisfying a higher-dimensional version of
Ocneanu's tube algebra. This defines an algebraic structure extending the
Drinfel'd double. Its irreducible representations, labeled by two fluxes and
one charge, characterize the torus-excitations. The tensor product of such
representations is introduced in order to construct a basis for (3+1)d gauge
models which relies upon the fusion of the defect excitations. This basis is
defined on manifolds of the form $\Sigma \times \mathbb{S}_1$, with $\Sigma$ a
two-dimensional Riemann surface. As such, our construction is closely related
to dimensional reduction from (3+1)d to (2+1)d topological orders.
