Question regarding lining hope chest with aromatic cedar

I am currently making a hope chest and need some advise on how to line it with aromatic cedar.

I have constructed the exterior case with solid red oak using frame and raised panel construction similar to kitchen cabinet doors and want to line the inside with cedar. i have constructed the bottom of the case using solid cedar and encased it in a dado allowing it to float to allow for expansion and contraction. The lining of the rest of the inside concerns me as to how I will allow for the inevitable movement of the cedar. I cannot simply glue it in place as this would create a cross grain situation with the stiles of the exterior cabinet.'

Any suggestions would be most appreciated.

Thanks in advance for your help.