NOVELTY - A positive electrode active material for a lithium ion battery comprises a layered lithium metal oxide.    USE - As positive electrode active material for a lithium ion battery (claimed) useful in mobile communication devices such as phones, mobile entertainment devices such as media player 3 (MP3) players and televisions, portable computers, as well as in transportation devices such as automobiles and fork lifts, in vehicle applications such as in battery packs for hybrid vehicles, plug-in hybrid vehicles and purely electric vehicles.    ADVANTAGE - The materials form a layer-layer composite crystal structure that has very good cycling properties at high voltages, although the materials exhibit significant first cycle irreversible capacity loss. The lithium rich compositions undergo significant irreversible structural changes during the first charge cycle of the battery in which lithium is extracted from the active composition. The irreversible capacity losses are associated with changes in crystal structure or other side reactions, such as the formation of molecular oxygen. Nevertheless, the lithium rich compositions have significant increases in reversible specific capacity relative to the reference compositions that are not lithium rich, which makes these potentially important materials for battery applications. These lithium rich materials operate at relatively high voltages. Furthermore, the composite crystal structure provides greater stability with respect to cycling following the irreversible changes that take place during the first charge. Doping to replace some of the transition metals provides further stabilization and improves the performance of the compositions in lithium ion battery applications. Due to the high capacity of the batteries, a battery pack that yields a desired amount of total power can be made in a reasonable volume, and these battery packs can correspondingly achieve the excellent cycling performance.    DETAILED DESCRIPTION - A positive electrode active material for a lithium ion battery comprises a layered lithium metal oxide approximately represented by the formula xLi2MnO3.(1-x)LiNiu+ Delta Mnu- Delta -dLidCowAyO2 (I), where an optional fluorine dopant can replace not greater than 10 mole percent of the oxygen.    x=0.03-0.55;    d=0.004-0.25;    2u+w+y= approximately 1;    Delta =-0.3 to 0.3;    w=0-1;    u= 0-0.5;    y=0-0.1;and    A1=Mg, Sr, Ba, Cd, Zn, Al, Ga, B, Zr, Ti, Ca, Ce, Y, Nb, Cr, Fe, and/or V.    Provided that both (u Delta + Delta ) and w are not both 0. INDEPENDENT CLAIMS are included for the following:    (1) positive electrode (104) for a lithium-based battery, where the electrode comprising the positive electrode active material, distinct electrically conductive powder (1-25 wt.%) and a polymer binder;    (2) a lithium-based battery (100) comprising a negative electrode (102), a positive electrode (104), a separator (106) between the positive electrode and the negative electrode and an electrolyte comprising lithium ions; and    (3) forming a lithium doped, lithium rich metal oxide composition either involving: precipitating a metal precursor compound comprising a selected amount of lithium dopant and transition metal elements in selected amounts; and calcining at a first temperature a mixture of lithium carbonate and the precursor metal compound to form the lithium doped, lithium rich metal oxide composition; or involving: heating a blend of lithium carbonate with a lithium rich metal oxide to form a doped composition, where the lithium carbonate is in an amount to provide lithium element at a selected dopant stoichiometry.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic drawing of a battery structure separated from a container.    Battery (100)    Negative electrode (102)    Positive electrode (104)    Separator (106)    Current collectors (108)