  We investigate the confinement mechanism in three-flavor QCD with imaginary
isospin chemical potentials $(\mu_u,\mu_d,\mu_s)=(i\theta T,-i\theta T,0)$,
using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model, where $T$ is
temperature. As for three degenerate flavors, the system has $\mathbb{Z}_{3}$
symmetry at $\theta=2\pi/3$ and hence the Polyakov loop $\Phi$ vanishes there
for small $T$. As for 2+1 flavors, the symmetry is not preserved for any
$\theta$, but $\Phi$ becomes zero at $\theta=\theta_{\rm conf} < 2\pi/3$ for
small $T$. The confinement phase defined by $\Phi=0$ is realized, even if the
system does not have $\mathbb{Z}_{3}$ symmetry exactly. In the $\theta$-$T$
plane, there is a critical endpoint of deconfinement transition. The
deconfinement crossover at zero chemical potential is a remnant of the
first-order deconfinement transition at $\theta=\theta_{\rm conf}$. The
relation between the non-diagonal element $\chi_{us}$ of quark number
susceptibilities and the deconfinement transition is studied. The present
results can be checked by lattice QCD simulations directly, since the
simulations are free from the sign problem for any $\theta$.
