Is there an adhesive material I can print high quality artwork on?

I sell acrylic display cases like the ones that can be seen here: ToyKick.com.

I would like to start offering cases with backgrounds. As seen here: http://bit.ly/Ks7fMq

I have some artwork I would like to attach to the back of my cases. I need to be able to attach it well so that it is strong and looks professional – I prefer to stay away from glue and tape if I can.

I am wondering if there is a material I can print on that will stick to the back of the acrylic case.

Since I am sticking the material to the outside back of the case and the case is facing inward, I would need the adhesive side and the printed side to be the same side. In other words, I would need to PRINT ON THE STICKY.

Does anyone know of a solution for what I am trying to accomplish. Added a background should be a permanent thing if possible.