Let $G$ be an arbitrary (discrete) group. It acts by left translation on $\ell^\infty(G)$. The uniform Roe algebra of $G$ is defined as the crossed product $\ell^\infty (G) \rtimes_{\mathrm{red}}G$.

Elmar Thoma has shown (*Thoma, E.*, **Eine Charakterisierung diskreter Gruppen vom Typ I**, Invent. Math. 6, 190-196 (1968). ZBL0169.03802.) that the reduced group $C^*$-algebra $C_{\mathrm{red}}^*(G)$ of a group $G$ is a type I $C^*$-algebra (i.e. there exists some $n\in \mathbb{N}$ such that for every irreducible representation $\pi$ of $C_{\mathrm{red}}^*(G)$ the dimension of the corresponding Hilbert space is less or equal to $n$) if and only if $G$ is virtually abelian.

I'm wondering if for virtually abelian groups the corresponding uniform Roe algebra must also be of type I. Does a result into that direction exist?