Something like this?
paper-cut-chinese-character_~u10454105[1].jpg
It's probably a touristy-type thing that didn't cost much and probably comes in a see-through sleeve?
Slide it out of its sleeve and you've got something that can just blow away or fold if you have a bit of a draught - not that easy to handle.
You could apply tiny/strategic dabs of adhesive, but no matter what type you use, evo-stick or starch paste, some can ooze out on to the front, or even seep through - it's a tricky operation, plus expansion/contraction could shred it as it's so flimsy.
If you peeled the protective sheet from a piece of acrylic and laid this thing on it, the static would probably hold it for eternity. If you laid it on top of a piece of felt and turned it upside down, it probably would not fall off.
So, I'd use that combination of static and grab, an overlay of acrylic and a mount covered in light wadding and then with a fabric with some 'tooth' like velvet, velour, suedette. The overlay could be under a window mount (mat) with glazing over that, or not, but (ideally) that acrylic would be AR (abrasion resistant) - or, if it's not a big thing, a Melinex overlay might work, as long as the shape is a regular one.
Failing all that you could just mount it in the plastic wallet that it came in, but that will probably yellow and/or go brittle quite quickly.