We report the structure and stability of ceria units deposited on the surface of γ-Al2O3 or incorporated in its cavities, as determined by periodic density functional calculations. Ceria species are modeled as CeO2 or Ce2O4 moieties or as a small nanoparticle, Ce13O26, on the (100) and (001) surfaces of a γ-Al2O3 slab. Among the studied structures the incorporation of Ce(4+) ions in cavities of γ-Al2O3 is favored with respect to the ions on the surface only in subsurface cavities of the (100) surface. The calculations also suggested that formation of a surface layer of ceria on the (100) alumina surface is preferable compared to three-dimensional moieties. The deposition of a small ceria nanoparticle on (100) and (001) surfaces of γ-Al2O3 reduces the energy for oxygen vacancy formation to an essentially spontaneous process on the (100) surface, which may be the reason for the experimentally detected large fraction of Ce(3+) ions in the CeO2/γ-Al2O3 systems. The deposition of a single rhodium atom or RhO unit in some of the structures with a CeO2 unit and Ce13O26 showed that spontaneous electron transfer from rhodium to cerium ion occurs, which results in reduction of Ce(4+) to Ce(3+) and the oxidation of rhodium. Only in the presence of deposited rhodium atoms, the incorporated cerium ions can be reduced to Ce(3+).