Free wreath products by finite group duals

Let $\mathbb G$ be a compact quantum group and let $Λ$ be a finite group. We study $\mathbb W(\mathbb G,Λ):=\mathbb G\wr_{*,β_Λ}\widehatΛ$, a natural family parallel to Bichon's free wreath products $\mathbb G\wr_*S_N^+$. We obtain an explicit formula for the Haar state of $\mathbb W(\mathbb G,Λ)$.