  We present a new version of a semi-analytic model of cosmological galaxy
formation, incorporating a star formation law with a feedback depending on the
galaxy-scale mean dust opacity and metallicity, motivated by recent
observations of star formation in nearby galaxies and theoretical
considerations. This new model is used to investigate the effect of such a
feedback on shaping the galaxy luminosity function and its evolution. Star
formation activity is significantly suppressed in dwarf galaxies by the new
feedback effect, and the faint-end slope of local luminosity functions can be
reproduced with a reasonable strength of supernova feedback, which is in
contrast to the previous models that require a rather extreme strength of
supernova feedback. Our model can also reproduce the early appearance of
massive galaxies manifested in the bright-end of high redshift K-band
luminosity functions. Though some of the previous models also succeeded in
reproducing this, they assumed a star formation law depending on the
galaxy-scale dynamical time, which is not supported by observations. We argue
that the feedback depending on dust opacity (or metal column density) is
essential, rather than that simply depending on gas column density, to get
these results.
