  Recent observations of Type Ia supernovae (SNe Ia) suggest that some of the
progenitor white dwarfs (WDs) had masses up to 2.4-2.8 M_sun, highly exceeding
the Chandrasekhar mass limit. We present a new single degenerate (SD) model for
SN Ia progenitors, in which the WD mass possibly reaches 2.3-2.7 M_sun. Three
binary evolution processes are incorporated; optically thick winds from
mass-accreting WDs, mass-stripping from the binary companion star by the WD
winds, and WDs being supported by differential rotation. The WD mass can
increase by accretion up to 2.3 (2.7) M_sun from the initial value of 1.1 (1.2)
M_sun, being consistent with high luminosity SNe Ia such as SN 2003fg, SN
2006gz, SN 2007if, and SN 2009dc. There are three characteristic mass ranges of
exploding WDs. In an extreme massive case, differentially rotating WDs explode
as an SN Ia soon after the WD mass exceeds 2.4 M_sun because of a secular
instability at T/|W|\sim 0.14. For a mid mass range of M_WD=1.5-2.4 M_sun, it
takes some time (spinning-down time) until carbon is ignited to induce an SN Ia
explosion after the WD mass has reached maximum, because it needs a loss or
redistribution of angular momentum. For a lower mass case of rigidly rotating
WDs, M_WD=1.38-1.5 M_sun, the spinning-down time depends on the timescale of
angular momentum loss from the WD. The difference in the spinning-down time may
produce the "prompt" and "tardy" components. We also suggest the very bright
super-Chandrasekhar mass SNe Ia are born in a low metallicity environment.
