Li-rich layered oxides Li_1+xM_1-xO₂ (0<x<0.33), where M=Co, Mn, Ni, have emerged as promising cathode materials, because they can deliver much higher capacities (> 250 mAh/g) than the conventional LiCoO₂ cathode. Important issues relate to what is the origin of the electrochemical activity and high capacity? In this work, possible charge compensation mechanisms upon lithium extraction from Li₂MnO₃ are studied by ab-initio density functional theory calculations: (a) Reversible oxidation of bulk O^2- to other anion species such as superoxide or peroxide; (b) Loss of lattice oxygen (oxygen evolution). Both thermodynamic (reaction enthalpies and electrochemical potentials) and kinetic (ion migration) aspects are investigated.