Molecular adsorption (MA) and dissociative adsorption (DA) of O₂ on in complexes of a model nanoparticle Ce₂₁O₄₂ (NP) with an atom and small clusters of silver have been addressed. According to results of density functional calculations formation energies of such systems (with respect to the non-interacting NP, Ag_n and O₂) are calculated to be 2.0-4.4 eV. O₂ adsorption energy (E_ad(O₂)) in the lowest-energy atomic complex with О₂ in a bridging position between Ce ion and Ag bound on the {111} nanofacet (AgOO{Ce}-complex) is as high as ~1.3 eV. Ag_nOO{Ce}- и OAg_nO{Ce}- bridging structures are formed in MA and DA lowest-energy complexes of Ag₃ on {100} and {111} as well as Ag₄ on {100} nanofacets. Bonding characteristics of the Ag_nOO{Ce}-structures match those for stable superoxo groups О₂^-. E_ad(О₂) of the lowest-energy МА and DA complexes of O₂ with Ag clusters are in the range of 0.5-1.1 and 1.4-2.0 eV, respectively. Activation energies for O₂ dissociation in Ag_nOO{Ce}-complexes (n=3,4) calculated to be 1.5-2.1 eV indicate low rates of these oxidation rearrangements.