Repetitive higher cluster categories of type Aₙ

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We show that the repetitive higher cluster category of type Aₙ, defined as the orbit category Dᵇ(mod kAₙ)/(tau⁻¹[m])ᵖ, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category Dᵇ(mod kAₙ).