  Several studies have tried to ascertain whether or not the increase in
abundance of the early-type galaxies (E-S0a's) with time is mainly due to major
mergers, reaching opposite conclusions. We have tested it directly through
semi-analytical modelling, by studying how the massive early-type galaxies with
log(M_*/Msun)>11 at z~0 (mETGs) would have evolved backwards-in-time, under the
hypothesis that each major merger gives place to an early-type galaxy. The
study was carried out just considering the major mergers strictly reported by
observations at each redshift, and assuming that gas-rich major mergers
experience transitory phases of dust-reddened, star-forming galaxies (DSFs).
The model is able to reproduce the observed evolution of the galaxy LFs at
z<~1, simultaneously for different rest-frame bands (B, I, and K) and for
different selection criteria on color and morphology. It also provides a
framework in which apparently-contradictory results on the recent evolution of
the luminosity function (LF) of massive, red galaxies can be reconciled, just
considering that observational samples of red galaxies can be significantly
contaminated by DSFs. The model proves that it is feasible to build up ~50-60%
of the present-day mETG population at z<~1 and to reproduce the observational
excess by a factor of ~4-5 of late-type galaxies at 0.8<z<1 through the
coordinated action of wet, mixed, and dry major mergers, fulfilling global
trends that are in general agreement with mass-downsizing. The bulk of this
assembly takes place during ~1 Gyr elapsed at 0.8<z<1. The model suggests that
major mergers have been the main driver for the observational migration of mass
from the massive-end of the blue galaxy cloud to that of the red sequence in
the last ~8 Gyr.(Abridged)
