  Stacking cosmic microwave background (CMB) maps around known galaxy clusters
and groups provides a powerful probe of the distribution of hot gas in these
systems via the Sunyaev-Zel'dovich (SZ) effect. A stacking analysis allows one
to detect the average SZ signal around low mass halos, and to extend
measurements out to large scales, which are too faint to detect individually in
the SZ or in X-ray emission. In addition, cross correlations between SZ maps
and other tracers of large-scale structure (with known redshifts) can be used
to extract the redshift-dependence of the SZ background. Motivated by these
exciting prospects, we measure the two-point cross-correlation function between
a catalog of $\sim 380,000$ galaxy groups (with redshifts spanning
$z=0.01-0.2$) from the Sloan Digital Sky Survey (SDSS) and Compton-y parameter
maps constructed by the Planck collaboration. We find statistically significant
correlations between the group catalog and Compton-y maps in each of six
separate mass bins, with estimated halo masses in the range $10^{11.5-15.5}
M_\odot/h$. We compare these measurements with halo models of the SZ signal,
which describe the stacked measurement in terms of one-halo and two-halo terms.
The one-halo term quantifies the average pressure profile around the groups in
a mass bin, while the two-halo term describes the contribution of correlated
neighboring halos. For the more massive groups we find clear evidence for the
one- and two-halo regimes, while groups with mass below $10^{13} M_\odot/h$ are
dominated by the two-halo term given the resolution of Planck data. We use the
signal in the two-halo regime to determine the bias-weighted electron pressure
of the universe: $\langle b P_e \rangle= 1.50 \pm 0.226 \times 10^{-7}$ keV
cm$^{-3}$ (1-$\sigma$) at $z\approx 0.15$.
