Let \(U\) be the distribution algebra of a reductive algebraic group over a field of characteristic \(p > 0\), with triangular decomposition \(U \cong U^+ \otimes U^0 \otimes U^-\). This article is concerned with the structure of the category \(\mathcal{O}\) of locally \(U^+\)-finite \(U\)-modules that admit a weight space decomposition. For every locally closed set \(K\) of weights, there is a Serre subquotient category \(\mathcal{O}_{[K]}\) of \(\mathcal{O}\) with simple objects indexed by \(K\), and motivated by Steinberg’s tensor product theorem, the main result of the article establishes a periodicity property of these subquotient categories. Namely, if \(l > 0\) such that \(K \cap ( K - p^l ) \cdot \nu = \varnothing\) for all weights \(\nu > 0\) then \(\mathcal{O}_{[K]}\) is equivalent to \(\mathcal{O}_{[ K + p^l \cdot \gamma ]}\) for all dominant weights \(\gamma\). The equivalence is induced by taking tensor products with the \(l\)-fold Frobenius twist of the simple \(U\)-module \(L(\gamma)\) of highest weight \(\gamma\). The author also states and proves other basic properties of the category \(\mathcal{O}\), such as the existence of Krull-Remak-Schmidt decompositions, the existence of projectives in truncated subcategories, a BGGH-reciprocity, and additional results on modules admitting a Verma flag.