The purpose of this paper is to demonstrate that solar cycle variations of the cross helicity of the Alfv¿nic turbulence can be the cause of the solar modulation of the galactic cosmic rays and its charge dependence if combined with nonvanishing magnetic helicity values of the turbulence. It is argued that the ratio of forward propagating Alfv¿n waves originating on the Sun to the total intensity is high at solar maxima and low at solar minima, whereas the intensity of backward moving waves probably originating by the pickup ion instability stays constant on time scales long compared to the 11-year periodicity. Our explanation fulfills the observational constraints that the average solar wind speed stays constant and that the total level of magnetic fluctuation power remains constant within 25% during the solar cycle. ¿American Geophysical Union 1991