  We use galaxy groups selected from the Sloan Digital Sky Survey (SDSS)
together with mass models for individual groups to study the galaxy-galaxy
lensing signals expected from galaxies of different luminosities and
morphological types. We compare our model predictions with the observational
results obtained from the SDSS by Mandelbaum et al. (2006) for the same samples
of galaxies. The observational results are well reproduced in a $\Lambda$CDM
model based on the WMAP 3-year data, but a $\Lambda$CDM model with higher
$\sigma_8$, such as the one based on the WMAP 1-year data,significantly
over-predicts the galaxy-galaxy lensing signal. We model, separately, the
contributions to the galaxy-galaxy lensing signals from different galaxies:
central versus satellite, early-type versus late-type, and galaxies in halos of
different masses. We also examine how the predicted galaxy-galaxy lensing
signal depends on the shape, density profile, and the location of the central
galaxy with respect to its host halo.
