We report four narrow peaks in the Ξ 0 b K − mass spectrum obtained using p p 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 m [ Ω b ( 6316 ) − ] = 6315.64 ± 0.31 ± 0.07 ± 0.50 MeV , m [ Ω b ( 6330 ) − ] = 6330.30 ± 0.28 ± 0.07 ± 0.50 MeV , m [ Ω b ( 6340 ) − ] = 6339.71 ± 0.26 ± 0.05 ± 0.50 MeV , m [ Ω b ( 6350 ) − ] = 6349.88 ± 0.35 ± 0.05 ± 0.50 MeV , where 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 Γ [ Ω b ( 6316 ) − ] < 2.8 MeV , Γ [ Ω b ( 6330 ) − ] < 3.1 MeV and Γ [ Ω b ( 6340 ) − ] < 1.5 MeV . The natural width of the Ω b ( 6350 ) − peak is 1.4 + 1.0 − 0.8 ± 0.1 MeV , which is 2.5 σ from zero and corresponds to an upper limit of 2.8 MeV. The peaks have local significances ranging from 3.6 σ to 7.2 σ . After accounting for the look-elsewhere effect, the significances of the Ω b ( 6316 ) − and Ω b ( 6330 ) − peaks are reduced to 2.1 σ and 2.6 σ , respectively, while the two higher mass peaks exceed 5 σ . The observed peaks are consistent with expectations for excited Ω − b resonances.