  In this article, we introduce halo products as a natural generalisation of
wreath products. They also encompass lampshuffler groups $\mathrm{FSym}(H)
\rtimes H$ and lampcloner groups $\mathrm{FGL}(H) \rtimes H$, as well as many
possible variations based for instance on braid groups, Thompson's groups,
mapping class groups, automorphisms of free groups. We build a geometric
framework that allows us to study the large-scale geometry of halo groups,
providing refined invariants distinguishing various halo groups up to
quasi-isometry.
