I've got a recessed light and I'm trying to figure out how to ground it properly.

The black and white wires are on one side of the back of the light and the ground wire is on the opposite side. The ground wire is riveted to the "can" and is a very thin, stranded copper wire that is also rather short. So it's difficult to get all three wires into a box. I can put the black and white into one side of the box and the ground in the other side.

My questions are:
1. Is it okay to put a bare copper wire into a box and terminate it to the solid copper ground wire?
2. The clamp on the box is designed for thick wire and doesn't clamp the thin copper ground wire, is this okay or is there another fitting?