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We show that the radial MASA in the orthogonal free quantum group algebraL(FO_N) is maximal amenable if N is large enough, using the AsymptoticOrthogonality Property. This relies on a detailed study of the correspondingbimodule, for which we construct in particular a quantum analogue ofR\u{a}dulescu's basis. As a byproduct we also obtain the value of thePuk\'anszky invariant for this MASA.

Maximal amenability of the radial subalgebra in free quantum group factors