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 Ce⁴⁺ 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 Ce³⁺ 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 Ce⁴⁺ to Ce³⁺ and the oxidation of rhodium. Only in the presence of deposited rhodium atoms, the incorporated cerium ions can be reduced to Ce³⁺.