  [Abbreviated] We have investigated the color-magnitude diagram of Omega
Centauri and find that the blue main sequence (bMS) can be reproduced only by
models that have a of helium abundance in the range Y=0.35-$0.40. To explain
the faint subgiant branch of the reddest stars ("MS-a/RG-a" sequence),
isochrones for the observed metallicity ([Fe/H]\approx0.7) appear to require
both a high age (~13Gyr) and enhanced CNO abundances ([CNO/Fe]\approx0.9$).
Y~0.35 must also be assumed in order to counteract the effects of high CNO on
turnoff colors, and thereby to obtain a good fit to the relatively blue turnoff
of this stellar population. This suggest a short chemical evolution period of
time (<1Gyr) for Omega Cen. Our intermediate-mass (super-)AGB models are able
to reproduce the high helium abundances, along with [N/Fe]~2 and substantial O
depletions if uncertainties in the treatment of convection are fully taken into
account. These abundance features distinguish the bMS stars from the dominant
[Fe/H] $\approx1.7$ population. The most massive super-AGB stellar models
(M_zams>=6.8M_sun, M_He,core>=1.245M_sun) predict too large N-enhancements,
which limits their role in contributing to the extreme populations. We show
quantitatively that highly He- and N-enriched AGB ejecta have particularly
efficient cooling properties. Based on these results and on the reconstruction
of the orbit of Omega Cen with respect to the Milky Way we propose the galactic
plane passage gas purging scenario for the chemical evolution of this cluster.
Our model addresses the formation and properties of the bMS population
(including their central location in the cluster). We follow our model
descriptively through four passage events, which could explain not only some
key properties of the bMS, but also of the MS-a/RGB-a and the s-enriched stars.
