I am up by a piece and close to winning but my opponent is putting my king in check over and over. My king is forced to make the same move every time, and then back to it's original position after the next check. We have made the same series of moves over 5 times now.

After you move, go back to the game screen--while it is your opponents move--and hit the "claim draw" button.

your opponent is entitled to draw at the third repitition if the same exact set up of peices on the board. If there is a claim draw box under the chat box one of you can hit it to end the game. if you are up let him figure it out. he may not, if he has done it 5 times. then if he moves elsewhere he is going to lose instead

You had an interesting win in there a bit earlier btw:  35... Qh1+ 36 Ke2 Qg2+ 37 Nf2 f3+ 38 Ke3 Bg5+ 39 Ke4 Rhe8+ 40 Kf5 g6+ 41 Kxg6 Bd2+.

37.  f3+!!!!

Very interesting line.  Thanks Andy.