  A partial wave analysis of $\chi_{c0}\to\pi^+\pi^-K^+K^-$ in
$\psi(2S)\to\gamma\chi_{c0}$ decay is presented using a sample of 14 million
$\psi(2S)$ events accumulated by the BES II detector. The data are fitted to
the sum of relativistic covariant tensor amplitudes for intermediate resonant
decay modes. From the fit, significant contributions to $\chi_{c0}$ decays from
the channels $f_0(980)f_0(980)$, $f_0(980)f_0(2200)$, $f_0(1370)f_0(1710)$,
$K^*(892)^0\bar K^*(892)^0$, $K^*_0(1430)\bar K^*_0(1430)$, $K^*_0(1430)\bar
K^*_2(1430) + c.c.$, and $K_1(1270)K$ are found. Flavor-SU(3)-violating
$K_1(1270)-K_1(1400)$ asymmetry is observed. Values obtained for the masses and
widths of the resonances $f_0(1710)$, $f_0(2200)$, $f_0(1370)$, and
$K^*_0(1430)$ are presented.
