  The molecular gas serves as a key probe of the complex interplay between
black hole accretion and star formation in the host galaxies of active galactic
nuclei (AGNs). We use CO(2-1) observations from a new ALMA survey, in
conjunction with literature measurements, to investigate the molecular gas
properties of a representative sample of 40 z<0.3 Palomar-Green quasars, the
largest and most sensitive study of molecular gas emission to date for nearby
quasars. We find that the AGN luminosity correlates with both the CO luminosity
and black hole mass, suggesting that AGN activity is loosely coupled to the
cold gas reservoir of the host. The observed strong correlation between host
galaxy total infrared luminosity and AGN luminosity arises from their common
dependence on the molecular gas. We argue that the total infrared luminosity,
at least for low-redshift quasars, can be used to derive reliable star
formation rates for the host galaxy. The host galaxies of low-redshift quasars
have molecular gas content similar to that of star-forming galaxies of
comparable stellar mass. Moreover, they share similar gas kinematics, as
evidenced by their CO Tully-Fisher relation and the absence of detectable
molecular outflows down to sensitive limits. There is no sign that AGN feedback
quenches star formation for the quasars in our sample. On the contrary, the
abundant gas supply forms stars prodigiously, at a rate that places most of
them above the star-forming main sequence and with an efficiency that rivals
that of starburst systems.
