Strongly aperiodic SFTs on generalized Baumslag-Solitar groups

We look at constructions of aperiodic subshifts of finite type (SFTs) on fundamental groups of graph of groups. In particular, we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by Whyte and on two constructions of strongly aperiodic SFTs on F-n x Z and BS(m, n) of our own. Our two constructions rely on a path-folding technique that lifts an SFT on Z(2) inside an SFT on F-n x Z or an SFT on the hyperbolic plane inside an SFT on BS(m, n). In the case of F-n x Z, the path folding technique also preserves minimality, so that we get minimal strongly aperiodic SFTs on unimodular GBS groups.