  We present a study of tidal debris associated with 126 nearby red galaxies
selected from the MUSYC and NDWFS surveys. In the full sample 67 galaxies (53%)
show morphological signatures of tidal interactions, consisting of broad fans
of stars, tails, and other asymmetries at very faint surface brightness levels.
When restricting the sample to the 86 bulge-dominated early-type galaxies the
fraction of tidally disturbed galaxies rises to 71%, which implies that for
every ``normal'' undisturbed elliptical there are two which show clear signs of
interactions. The tidal features are red and smooth, and often extend over >50
kpc. Of the tidally distorted galaxies about 2/3 are remnants and 1/3 are
interacting with a companion galaxy. The companions are usually bright red
galaxies as well: the median R-band luminosity ratio of the tidal pairs is
0.31, and the median color difference after correcting for the slope of the
color-magnitude relation is -0.02 in B-R. If the ongoing mergers are
representative for the progenitors of the remnants ~35% of bulge-dominated
galaxies experienced a merger with mass ratio >1:4 in the recent past. With
further assumptions it is estimated that the present-day mass accretion rate of
galaxies on the red sequence is 0.09+-0.04 per Gyr. For a constant or
increasing mass accretion rate with redshift, we find that red mergers may lead
to an evolution of a factor of >~2 in the stellar mass density in luminous red
galaxies over the redshift range 0<z<1, consistent with recent studies of the
evolution of the luminosity density. We conclude that most of today's field
elliptical galaxies were assembled at low redshift through "dry" mergers of
gas-poor, bulge-dominated systems. [ABRIDGED]
