  We investigate which conditions of dust attenuation and stellar populations
allow models of dusty, continuously star-forming, bulge-less disk galaxies at
0.8<z<3.2 to meet the different colour selection criteria of high-z ``red''
galaxies (e.g. Rc-K>5.3, Ic-K>4, J-K>2.3). As a main novelty, we use stellar
population models that include the thermally pulsating Asymptotic Giant Branch
(TP-AGB) phase of stellar evolution. The star formation rate of the models
declines exponentially as a function of time, the e-folding time being longer
than 3 Gyr. In addition, we use calculations of radiative transfer of the
stellar and scattered radiation through different dusty interstellar media in
order to explore the wide parameter space of dust attenuation. We find that
synthetic disks can exhibit red optical/near-infrared colours because of
reddening by dust, but only if they have been forming stars for at least about
1 Gyr. Extremely few models barely exhibit Rc-K>5.3, if the inclination i=90
deg and if the opacity 2*tauV>6. Hence, Rc-K-selected galaxies at 1<z<2 most
probably are either systems with an old, passively evolving bulge or
starbursts. Synthetic disks at 1<z<2 exhibit 4<Ic-K<4.8, if they are seen edge
on (i.e. at i about 90 deg) and if 2*tauV>0.5. This explains the large fraction
of observed, edge-on disk-like galaxies with Ks<19.5 and F814W-Ks>4. Finally,
models with 2<z<3.2 exhibit 2.3<J-K<3, with no bias towards i about 90 deg and
for a large range in opacity (e.g. 2*tauV>1 for i about 70 deg). In conclusion,
red disk-like galaxies at 0.8<z<3.2 may not necessarily be dustier than nearby
disk galaxies (with 0.5<2*tauV<2) and/or much older than about 1 Gyr. This
result is due both to a realistic description of dust attenuation and to the
emission contribution by TP-AGB stars... (Abridged)
