  In this work we investigate the characteristics of the group velocity of
obliquely propagating Alfv\'en waves in a dusty plasma typical of a stellar
wind. The dispersion relation is derived with the aid of the kinetic theory for
a magnetized dusty plasma consisting of electrons and ions, with distribution
of momenta described by a Maxwellian function. The dust particles are
considered to be immobile and have all the same size; they are electrically
charged by absorption of plasma particles via inelastic collisions and by
photoionization. We numerically solve the dispersion relation and calculate the
components of group velocity (along and transverse to the magnetic field) for
the normal modes, namely the compressional and shear Alfv\'en waves (CAW and
SAW). The results show that the direction of the group velocity of CAWs is
greatly modified with the wave-vector direction. On the other hand, SAWs will
present group velocity propagating practically along the magnetic field. The
changes in dust parameters, such as number density and equilibrium electrical
charge, may significantly change the waves' characteristics. It is seen that
for sufficiently high dust to ion number density ratio, the SAWs may present
perpendicular group velocity propagating in opposite direction to the
perpendicular phase velocity, in a small interval of wavenumber values; we also
notice that this interval may change, or even vanish, when the flux of
radiation incident on the dust is altered, changing the equilibrium electrical
charge of the grains.
