  We address the fundamental question of matching the rest-frame K-band
luminosity function (LF) of galaxies over the Hubble time using semi-analytic
models, after modification of the stellar population modelling. We include the
Maraston evolutionary synthesis models, that feature a higher contribution by
the Thermally Pulsating - Asymptotic Giant Branch (TP-AGB) stellar phase, into
three different semi-analytic models, namely the De Lucia and Blaizot version
of the Munich model, MORGANA and the Menci model. We leave all other input
physics and parameters unchanged. We find that the modification of the stellar
population emission can solve the mismatch between models and the observed
rest-frame K-band luminosity from the brightest galaxies derived from UKIDSS
data at high redshift. For all explored semi-analytic models this holds at the
redshifts - between 2 and 3 - where the discrepancy was recently pointed out.
The reason for the success is that at these cosmic epochs the model galaxies
have the right age (~1 Gyr) to contain a well-developed TP-AGB phase which
makes them redder without the need of changing their mass or age. At the same
time, the known overestimation of the faint end is enhanced in the K-band when
including the TP-AGB contribution. At lower redshifts (z<2) some of the
explored models deviate from the data. This is due to too short merging
timescales and inefficient 'radio-mode' AGN feedback. Our results show that a
strong evolution in mass predicted by hierarchical models is compatible with no
evolution on the bright-end of the K-band LF from z=3 to the local universe.
This means that, at high redshifts and contrary to what is commonly accepted,
K-band emission is not necessarily a good tracer of galaxy mass.
