We consider the excitation of convective cells in the parametric decay of finite amplitude (inertial) Alfv¿n waves. We formulate a set of coupled equations describing the nonlinear interaction of Alfv¿n waves and the electrostatic convective mode and obtain the nonlinear dispersion relation for electrostatic convection cells. Generation of convection cells takes place only when dispersive effects due to the electron skin depth come into play. The generation of such cells is due to the Reynolds stresses of short-scale Alfv¿n waves. These are nonzero when the perpendicular Alfv¿n wavelengths are of the order of the collisionless electron skin depth. The convective cells are nonoscillatory two-dimensional modes with wave vector perpendicular to that of the pump Alfv¿n wave. The nonlinear growth rate of these cells is a sensitive function (proportional to k5) of the wave number k of the Alfv¿nic pump wave. This implies that the instability transfers wave energy from the short wavelength regime of the inertial Alfv¿n wave to the long wavelength regime of the convective cells which is typical for an inverse turbulent cascade. We also discuss the relation of the new parametric regime to the parametric wave-wave interaction of two counterstreaming inertial Alfv¿n waves. Application to satellite observations of inertial Alfv¿n waves in the auroral ionosphere shows agreement of the scales and explains the observed large amplitudes of the waves. It is shown that convective cells produced by the parametric instability could cause the fine structure of the turbulent Alfv¿n boundary layer and can play an important role in the ionospheric plasma turbulence as well as the energy source for auroral structures.