  The M\"{o}bius strip, a long sheet of paper whose ends are glued together
after a $180^{\circ}$ twist, has remarkable geometric and topological
properties. Here, we consider dielectric M\"{o}bius strips of finite width and
investigate the interplay between geometric properties and resonant light
propagation. We show how the polarization dynamics of the electromagnetic wave
depends on the topological properties, and demonstrate how the geometric phase
can be manipulated between $0$ and $\pi$ through the system geometry. The loss
of the M\"{o}bius character in thick cavities and for small twist segment
lengths allows one to manipulate the polarization dynamics and the far-field
emission, and opens the venue for applications.
