Homotopy types of gauge groups over non-simply-connected closed 4-manifolds

Let $G$ be a simply-connected simple compact Lie group and let $M$ be an orientable smooth closed 4-manifold. In this paper we calculate the homotopy type of the suspension of $M$ and the homotopy types of the gauge groups of principal $G$-bundles over $M$ when $pi_1(M)$ is: (1)~$mathbb{Z}^{*m}$, (2)~$mathbb{Z}/p^rmathbb{Z}$, or (3)~$mathbb{Z}^{*m}*(*^n_{j=1}mathbb{Z}/p_j^{r_j}mathbb{Z})$, where $p$ and the $p_j$s are odd primes.