We consider a symmetric elliptic operator, D, on a complete Riemannian manifold which admits a properly discontinuous action of a group $\Gamma $, with compact quotient. We assume that D is “gauge periodic” i.e. commutes with the group action twisted by a gauge ; a typical example is the Schrödinger operator with constant magnetic field. We associate a $C^*$-algebra with this situation and prove that the spectrum of (the closure) D has band sructure if this $C^*$-algebra has the “Kadison property”. For the magnetic Schrödinger operator, we can derive an optimal upperbound on the number of gaps for rational flux.