  Let $G$ be an affine algebraic group scheme over an algebraically closed
field $k$ of characteristic $p>0$, and let $G_r$ denote the $r$-th Frobenius
kernel of $G$. Motivated by recent work of Friedlander, the authors investigate
the class of mock injective $G$-modules, which are defined to be those rational
$G$-modules that are injective on restriction to $G_r$ for all $r\geq 1$. In
this paper the authors provide necessary and sufficient conditions for the
existence of non-injective mock injective $G$-modules, thereby answering a
question raised by Friedlander. Furthermore, the authors investigate the
existence of non-injective mock injectives with simple socles. Interesting
cases are discovered that show that this can occur for reductive groups, but
will not occur for their Borel subgroups.
