  We previously reported a significant clustering of red galaxies (R-K=3.5--6)
around the radio-loud quasar B2 1335+28 at z=1.086. In this paper, we establish
the existence of a rich cluster at the quasar redshift, and study the
properties of the cluster galaxies through further detailed analysis of the
photometric data. The color distribution of the galaxies in the cluster is
quite broad and the fraction of blue galaxies (\sim 70%) is much larger than in
intermediate-redshift clusters. Using evolutionary synthesis models, we show
that this color distribution can be explained by galaxies with various amounts
of star-formation activity mixed with the old stellar populations. Notably,
there are about a dozen galaxies which show very red optical-NIR colors but
also show significant UV excess with respect to passive-evolution models. They
can be interpreted as old early-type galaxies with a small amount of star
formation. The fact that the UV-excess red galaxies are more abundant than the
quiescent red ones suggests that a large fraction of old galaxies in this
cluster are still forming stars to some extent. However, a sequence of
quiescent red galaxies is clearly identified on the R-K versus K
color-magnitude (C-M) diagram. The slope and zero point of their C-M relation
appear to be consistent with those expected for the precursors of the C-M
relation of present-day cluster ellipticals when observed at z=1.1. We estimate
the Abell richness class of the cluster to be R \sim 1. New X-ray data
presented here place an upper limit of L_x < 2 10^{44} erg s^{-1} for the
cluster luminosity. Inspections of the wider optical images reveal some lumpy
structure, suggesting that the whole system is still dynamically young.
