Have stored my 40 year old Gresoppa Finse Skiis outside in the shed for the last 4 years since renovating our garage, exposing them to much lower temperatures and drier air. The lignostone edges have started separating at the tips and the tails, but have glued them back down at the beginning of each season. Have another pair of back country skis and only use the old skis to show off a couple times each year. This year I notice long a linear crack in the surface of one the skis that appears to extend to the base. Have a notion to apply epoxy on the surface or glue a piece of birch or ash to the surface, but imagine it will pop off as soon as the ski flexes with use. No argument that the skis have long outlived their expected use and should be a wall decoration. Any suggestions regarding a repair?

I don't know about how best to repair- maybe a little fiberglass w/epoxy but you will have to mar your skis by roughing up the surface with sandpaper before application. More importantly let your skis sit in the snow for a few days before use to bring moisture into the wood reducing the chance of the dry fracture.

It's possible that injecting West G/flex epoxy into the cracks would stop them from widening while remaining flexible. It would take some particular care when applying to avoid a mess on the surrounding areas. It would be a struggle to force the epoxy through a needle small enough for the job.

West G/flex

Personally I would retire them and look for replacements on Facebook Marketplace and Craigslist in your area. As a certain movie character might have put it, "there are lots and lots of them" there.