  Let $G$ be an affine algebraic group over an algebraically closed field of
positive characteristic. Recent work of Hardesty, Nakano, and Sobaje gives
necessary and sufficient conditions for the existence of so-called mock
injective $G$-modules, that is, modules which are injective upon restriction to
all Frobenius kernels of $G$. In this paper, we give analogous results for
contramodules, including showing that the same necessary and sufficient
conditions on $G$ guarantee the existence of mock-projective contramodules. In
order to do this we first develop contramodule analogs to many well-known
(co)module constructions.
