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Stable Cellularity in Hopfological Algebra

Let $H$ be a nontrivial finite-dimensional nonnegatively graded connected Hopf algebra, with $\ell=\max\{d:H_d\ne0\}$, and let $A\ge0$ be a locally finite $H$-module algebra with finite-dimensional split semisimple, $H$-trivial $A_0$. Under the gap $A_d=0$ for $0<d<\ell$, the shifted standard cells $\{q^{-r}Ae_x:0\le r...