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No, using wallpaper behind a stove top is not advised for the reason that you mentioned - it is a flammable material. Even though it might be temping to put it up as it looks attractive, in the interests of safety, (for yourself and others) install it somewhere else.
Regardless of whether you cook or bake often or not, fires in the home that start from a stove top can be damaging and cause injury.
Yes, choose a separate flame retardant wall covering for around the stove.
I really dont think wall paper is a suitable option. A backdoor will need to be washed on a regular basis and wallpaper is not that hardy.
Have you thought of using tin ceiling tiles instead. They are easy to use and can be glued in place.
I wonder if maybe you could wallpaper then attach a piece of glass over the section behind the stove. Research would be required to make sure that’s a safe and viable option.