The seven lowest adiabatic potential energy surfaces (PES) of the (Kr-O-2)(+) cluster ion in each of the (2)A" and (2)A’ symmetries are calculated. The computational method involves configuration interaction calculations in a basis of a thousand projected valence-bond state functions. It resorts to diagonal corrections of the Hamiltonian matrix prior to configuration interaction and makes use of an l-dependent pseudopotential for Kr. The results are characterized by the shallowness of the 1 (2)A" potential well and the absence of wells in the other PES investigated. The 1(2)A" equilibrium characteristics differ significantly from those proposed in other work. Notable effects on all the PES are observed when the O-O bond is stretched beyond 2.5a(0). No 1 (2)A’-2 (2)A’ (nor 1 (2)A"-2 (2)A") pseudocrossings are found that could explain, on the basis of mere electronic structure arguments, the available thermal energy charge transfer data. A 2 (2)A"-1 (2)A’ crossing actually exists but the related Coriolis coupling mechanism cannot be invoked for low energy <1 eV encounters. This draws attention to alternative more subtle dynamic charge transfer mechanisms possibly involving quartet-doublet spin-orbit transitions and/or (near) degeneracies of rovibronic, instead of mere electronic, energy levels. Evidence is shown for pseudocrossing mechanisms of population sharing between the 2,3A" and 2A’ states. Similar evidence is shown for an O-2(X (3) Sigma(g)(-))-->O-2(a (1) Delta g) excitation involving two electron rearrangement.