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Stacking cosmic microwave background (CMB) maps around known galaxy clustersand groups provides a powerful probe of the distribution of hot gas in thesesystems via the Sunyaev-Zel'dovich (SZ) effect. A stacking analysis allows oneto detect the average SZ signal around low mass halos, and to extendmeasurements out to large scales, which are too faint to detect individually inthe SZ or in X-ray emission. In addition, cross correlations between SZ mapsand other tracers of large-scale structure (with known redshifts) can be usedto extract the redshift-dependence of the SZ background. Motivated by theseexciting prospects, we measure the two-point cross-correlation function betweena 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 parametermaps constructed by the Planck collaboration. We find statistically significantcorrelations between the group catalog and Compton-y maps in each of sixseparate 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 ina mass bin, while the two-halo term describes the contribution of correlatedneighboring halos. For the more massive groups we find clear evidence for theone- and two-halo regimes, while groups with mass below $10^{13} M_\odot/h$ aredominated by the two-halo term given the resolution of Planck data. We use thesignal in the two-halo regime to determine the bias-weighted electron pressureof the universe: $\langle b P_e \rangle= 1.50 \pm 0.226 \times 10^{-7}$ keVcm$^{-3}$ (1-$\sigma$) at $z\approx 0.15$.

A Measurement of the Galaxy Group-Thermal Sunyaev-Zel'dovich Effect Cross-Correlation Function