The radius of comparison for actions of Z^d on simple AH algebras

Given 0 \leq r’ \leq r \leq \infty, and d \in N, we construct a simple unital AH algebra A with stable rank one, and a pointwise outer action α: Z^d \to Aut(A), such that rc(A)=r and rc (A \rtimes_α Z^d)=r’.