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We construct blocks of finite groups with arbitrarily large$\mathcal{O}$-Morita Frobenius numbers. There are no known examples of twoblocks defined over $\mathcal{O}$ that are not Morita equivalent but thecorresponding blocks defined over $k$ are. Therefore, the above stronglysuggests that Morita Frobenius numbers are also unbounded, which would answer aquestion of Benson and Kessar.

Arbitrarily large $\mathcal{O}$-Morita Frobenius numbers