We present here our first results of simulating the solar wind-magnetosphere interaction with a new three-dimensional electromagnetic particle code. Hitherto such global simulations were done with MHD codes while lower-dimensional particle or hybrid codes served to account for microscopic processes and such transport parameters as have to be introduced ad hoc in MHD. Our kinetic model attempts to combine the macroscopic and microscopic tasks. It relies only on the Maxwell curl equations and the Lorentz equation for particles, which are ideally suited for computers. The preliminary results shown here are for an unmagnetized solar wind plasma streaming past a dipolar magnetic field. The results show the formation of a bow shock and a magnetotail, the penetration of energetic particles into cusp and radiation belt regions, and dawn-dusk asymmetries.