In recent experiments, the rotational alignment of the laser induced nonthermal desorption of CO adsorbed on an epitaxially grown film of Cr2O3(0001) has been studied [Beauport, Al-Shamery, and Freund, Chem. Phys. Lett. 256, 641 (1996)]. At low-rotational quantum numbers J, the molecules desorb like helicopters (J-vector perpendicular to the surface) while at high J-values cartwheel motion is preferred (J-vector parallel to the surface). These stereodynamic effects and the experimental state resolved velocity distributions of the desorbing species are simulated by means of an exact time-dependent wave packet method in three dimensions. As a basis for this quantum-mechanical treatment of the CO desorption ab initio potential energy surfaces (PES) were used. The PES for the electronic ground state of the CO-Cr2O3(0001) system has been calculated previously by Pykavy [Surf. Sci. 479, 11 (2001)] in an embedded cluster approach. As the intermediate state, generated by the laser irradiation, an internal CO excited state (5 sigma -->2 pi*) was considered. The PES of this a (3)Pi -like state of CO adsorbed on Cr2O3(0001) was calculated at the ab initio CASSCF-level. Our key findings in the subsequent wave packet calculations are (1) a high-dimensional treatment of the photodesorption process is very important in this system, essentially the angular coordinates, very often neglected in similar studies, are responsible for a "successful" desorption event; (2) the change from the strongly tilted equilibrium geometry in the electronic ground state to the preferred upright position in the electronically excited state after laser irradiation is essential for the mechanistic picture of the desorption process; (3) the experimental phenomemon of rotational alignment can only be explained if the topologies of the PES of both the electronically excited and the ground state are accounted for; (4) the lifetime of the CO*-intermediate is in the order of 10 fs; (5) the molecule-surface vibrations in the electronic ground state do not much influence the asymptotic results at the experimental temperature of T=100 K. However, the inclusion of excited levels of the hindered rotation helps to gain insight into the desorption mechanism on a microscopic level.