Transformation group C1-algebras with continuous trace

We obtain several results characterizing when transformation group C¹-algebras have continuous trace. These results can be stated most succinctly when ($\text{G, Ω}$) is second countable, and the stability groups are contained in a fixed abelian subgroup. In this case, $\text{C}{}^1\text{(G, Ω)}$ has continuous trace if and only if the stability groups vary continuously on Ω and compact subsets of Ω are wandering in an appropriate sense. In general, we must assume that the stability groups vary continuously, and if ($\text{G, Ω}$) is not second countable, that the natural maps of $\text{G}\text{S}{}_{\mathrm{x}}$ onto G · x are homeomorphisms for each x. Then $\text{C}{}^1\text{(G, Ω)}$ has continuous trace if and only if compact subsets of Ω are wandering and an additional C¹-algebra, constructed from the stability groups and Ω, has continuous trace.