Torsion in coinvariants of certain Cantor minimal $\mathbb{Z}^2$-systems

Let $G$ be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal $\mathbb{Z}$-systems associated with a $G$-valued cocycle. When $G$ is non-cyclic and the cocycle is non-degenerate, it will be shown that the skew product system has torsion in its coinvariants.