  The integrated line width derived from CO spectroscopy provides a powerful
tool to study the internal kinematics of extragalactic objects, including
quasars at high redshift, provided that the observed line width can be properly
translated to more conventionally used kinematical parameters of galaxies. We
show, through construction of a K-band CO Tully-Fisher relation for nearby
galaxies spanning a wide range in infrared luminosity, that the CO line width
measured at 20% of the peak intensity, when corrected for inclination and other
effects, successfully recovers the maximum rotation velocity of the disk. The
line width at 50% of the peak intensity performs much more poorly, in large
part because CO lines have a wide range of profiles, which are shown to vary
systematically with infrared luminosity. We present a practical prescription
for converting observed CO line widths into the stellar velocity dispersion of
the bulge (sigma), and then apply it to a sample of low-redshift (z < 0.2) and
high-redshift (1.4 < z < 6.4) quasars to study their host galaxies. Nearby
quasars roughly fall on the correlation between black hole mass and bulge
stellar velocity dispersion established for inactive galaxies, but the host
galaxies of the high-z quasars systematically deviate from the local M_BH-sigma
relation. At a given sigma, high-z quasars have black hole masses larger by a
factor of 4 relative to local galaxies, suggesting that early in the life-cycle
of galaxies the development of the bulge lags behind the growth of the central
black hole. An alternative explanation for these observations, which currently
cannot be ruled out rigorously, is that high-redshift quasars are
preferentially viewed at face-on orientations.
