What type of glue should I use to paste a vinyl sheet to a wall?
Yes, there is.  It comes in 11oz and 30 oz. cartridge tubes, as well as, 1 gal. and 4 gal. containers under the search heading "vinyl adhesive".

I've used it on shower surrounds, rolled vinyl flooring, and a faux leather vinyl wall covering.

I find the most important consideration, during application, is to spread the adhesive well, for even coverage, to avoid "high spots" that may be evident afterward.  A V-notch 3/16" x 5/32" cove base adhesive spreader works best but for large areas a 1/4" (or smaller) square notch trowel will do.

[Edit: oh, and a regular baking rolling pin or a similar type of roller on a pole will help ensure the finishing material is pressed into the adhesive.]

[2nd edit: when rolling, start in the center and work toward the edges to prevent air bubbles...as one would to hang wallpaper.]