When I start up Xephyr inside of X, my keyboard map becomes wonky mostly just for non-printing characters. I can't use arrow keys. According to xev, The down arrow gets mapped to Super_R. The up arrow is Print Screen. PgDown is mapped to "Menu". My keyboard works fine in the original X display (:0), but in the Xephyr subdisplay (:1), nothing else quite works right.
I don't have any funky xmodmap things going on in my main X display that I'm aware of. All I really do is
setxkbmap -option ctrl:swapcaps.