We report four narrow peaks in the Ξ 0 b K − mass spectrum obtained using pp collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb −1 recorded by the LHCb experiment. Referring to these states by their mass, the mass values are m½Ωwhere the uncertainties are statistical, systematic, and the last is due to the knowledge of the Ξ 0 b mass. The natural widths of the three lower mass states are consistent with zero, and the 90% confidence-level upper limits are determined to be Γ½Ω b ð6316Þ − < 2.8 MeV, Γ½Ω b ð6330Þ − < 3.1 MeV and Γ½Ω b ð6340Þ − < 1.5 MeV. The natural width of the Ω b ð6350Þ − peak is 1.4 þ1.0 −0.8 AE 0.1 MeV, which is 2.5σ from zero and corresponds to an upper limit of 2.8 MeV. The peaks have local significances ranging from 3.6σ to 7.2σ. After accounting for the look-elsewhere effect, the significances of the Ω b ð6316Þ − and Ω b ð6330Þ − peaks are reduced to 2.1σ and 2.6σ, respectively, while the two higher mass peaks exceed 5σ. The observed peaks are consistent with expectations for excited Ω − b resonances.