We present a quantum mechanical calculation of the resistivity of a strongly modulated two-dimensional electron gas in a perpendicular magnetic field. For lattice constants of the order of the Fermi wavelength the classical picture of commensurate orbits breaks down and the magnetic band structure gains considerable influence. As a characteristic feature the longitudinal magneto-resistivity shows oscillations with a leading period of one flux quantum per unit cell which have their origin in the magnetic band structure. We find that they do only weakly depend on temperature and electron density and discuss the resulting necessary conditions for experimental observation.