K-band galaxy number counts (GNCs) exhibit a slope change at K~17.5 mag not present in optical bands. To unveil the nature of this feature, we have derived the contribution of different galaxy types to the total K-band GNCs at 0.3<z<1.5 by redshift bins and compared the results with expectations from several galaxy evolutionary models. We show that the slope change is caused by a sudden swap of the galaxy population that numerically dominates the total GNCs (from quiescent E-S0s at K<17.5 mag to blue star-forming discs at fainter magnitudes), and that it is associated with a flattening of the contribution of the E-S0s at 0.6<z<1 to the total GNCs. We confirm previous studies showing that models in which the bulk of massive E-S0s have evolved passively since z>2 cannot predict the slope change, whereas those imposing a relatively late assembly on them (z<1.5) can reproduce it. The K-band GNCs by redshift bins and morphological types point to a progressively definitive build-up of ~50% of this galaxy population at 0.8<z<1.5, which can be explained only through the major mergers reported by observations. We conclude that the slope change in total K-band GNCs is a vestige of the definitive assembly of a substantial fraction of present-day massive E-S0s at 0.8<z<1.5.
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