Magnetic field induced edge currents propagate in opposite directions at opposite edges of a Hall bar. We consider a system that possesses just one edge: a Möbius stripe. We show that if the carrier mean free path is less than the width of the stripe, magnetic field induced edge currents vanish. Instead, a stationary charge density wave is formed. Its profile is governed by the interplay between the magnetic field dependence of the chemical potential and the screened Coulomb repulsion of charge carriers. This effect offers an experimental tool for studies of the electron density of states in two-dimensional crystal films.