  We show that the observed Velocity Dispersion Function of E/S0 galaxies
matches strikingly well the distribution function of virial velocities of
massive halos virializing at z > 1.5, as predicted by the standard hierarchical
clustering scenario in a \LambdaCDM cosmology, for a constant ratio sigma/V_vir
= 0.55 \pm 0.05, close to the value expected at virialization if it typically
occurred at z > 3. This strongly suggests that dissipative processes and later
merging events had little impact on the matter density profile. Adopting the
above sigma/V_vir ratio, the observed relationships between photometric and
dynamical properties which define the fundamental plane of elliptical galaxies,
such as the luminosity-sigma (Faber-Jackson) and the luminosity-effective
radius relations, as well as the M_BH-sigma relation, are nicely reproduced.
Their shapes turn out to be determined by the mutual feedback of star-formation
(and supernova explosions)and nuclear activity, along the lines discussed by
Granato et al. (2004). To our knowledge, this is the first semi-analytic model
for which simultaneous fits of the fundamental plane relations and of the
epoch-dependent luminosity function of spheroidal galaxies have been presented.
