  We investigate the finite-temperature quantum chromodynamics (QCD) on a
rotating lattice with $N_f=2+1$ staggered fermions and the projective plane
boundary condition. We observe a negative rotational rigidity (defined in the
main text) and a negative quark spin susceptibility associated with the chiral
vortical effect. In contrast to most of the effective model predictions, we
find that the chiral condensate decreases and the Polyakov loop increases with
imaginary rotation, implying a rotational catalysis of chiral symmetry breaking
and confinement by real rotation. We determine the phase boundaries for both
chiral and confinement-deconfinement phase transitions on the $\Omega_I$-$T$
plane, where $\Omega_I$ is the imaginary angular velocity.
