  We apply the recent results of Galkin et al. [GKMS15] to study some
geometrical features of Keum's fake projective planes. Among other things, we
show that the bicanonical map of Keum's fake projective planes is always an
embedding. Moreover, we construct a nonstandard exceptional collection on the
unique fake projective plane $X$ with $H_{1}(X;
\mathbb{Z})=(\mathbb{Z}/2\mathbb{Z})^{4}$.
