  We describe the structure present in algebras over the little disks operads
for various representations of a finite group $G$, including those that are not
necessarily universe or that do not contain trivial summands. We then spell out
in more detail what happens for $G=C_{2}$, describing the structure on algebras
over the little disks operad for the sign representation. Here we can also
describe the resulting structure in Bredon homology. Finally, we produce a
stable splitting of coinduced spaces analogous to the stable splitting of the
product, and we use this to determine the homology of the signed James
construction.
