  The critical behavior of an MN-component order parameter Ginzburg-Landau
model with isotropic and cubic interactions describing antiferromagnetic and
structural phase transitions in certain crystals with complicated ordering is
studied in the framework of the four-loop renormalization group (RG) approach
in $(4-2\ve)$-dimensions. Using dimensional regularization and the minimal
subtraction scheme, the perturbative expansions for RG functions are deduced
for generic M and N and resummed by the Borel transformation combined with a
conformal mapping. Investigation of the global structure of RG flows for the
physically significant cases M=2 and N=2, N=3 shows that the model has a
three-dimensionally stable fixed point different from the Bose one. The
critical dimensionality is proved to be exactly two times smaller than its
counterpart in the real cubic model: N_c^C ={1/2} N_c^R. The numerical value
$N_c^C=1.447 \pm 0.020$ is obtained from resumming the known five-loop
$\ve$-series for N_c^R. Since N_c^C < 2, the critical thermodynamics of the
model relevant to the phase transitions in real substances should be governed
by the complex cubic fixed point with a new set of critical exponents:
$\gm=1.404(25)$, $\nu=0.715(10)$, $\et=0.0343(20)$ for N=2 and $\gm=1.390(25)$,
$\nu=0.702(10)$, $\et=0.0345(15)$ for N=3.
