  We present an analysis of the z ~ 0 morphology-environment relation for 911
bright (M_B < -19) galaxies, matching classical RC3 morphologies to the
SDSS-based group catalog of Yang et al. We study how the relative fractions of
spirals, lenticulars, and ellipticals depend on halo mass over a range of
10^11.7-10^14.8 h^-1 Msol. We pay particular attention to how morphology
relates to central (most massive) vs satellite galaxy status. The fraction of
galaxies which are elliptical is a strong function of stellar mass; it is also
a strong function of halo mass, but only for central galaxies. We interpret
this in a scenario where elliptical galaxies are formed, probably via mergers,
as central galaxies within their halos; satellite ellipticals are previously
central galaxies accreted onto larger halos. The overall fraction of S0
galaxies increases strongly with halo mass, from ~10% to ~70%. We find striking
differences between the central and satellites: 20+/-2% of central M_* >
10^10.5 Msol galaxies are S0 regardless of halo mass, but satellite S0 galaxies
are only found in massive (> 10^13 h^-1 Msol) halos, where they are 69+/-4% of
the M_* > 10^10.5 Msol satellite population. This suggests two channels for S0
formation: one for central galaxies, and another which transforms lower mass
(M_* <~ 10^11 Msol) accreted spirals into satellite S0 galaxies in massive
halos. Analysis of finer morphological structure (bars and rings in disk
galaxies) shows some trends with stellar mass, but none with halo mass; this is
consistent with other recent studies which indicate that bars are not strongly
influenced by galaxy environment. Radio sources in high-mass central galaxies
are common, similarly so for elliptical and S0 galaxies, with a frequency that
increases with halo mass. Emission-line AGN (mostly LINERs) are more common in
S0s, but show no strong environmental trends (abridged).
