take them to your local shop, it probably wont work, but its worth a try. K2 is a huge company, so the chances are good.
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core shots would not be covered under warranty their going to assume he went over rocks if the base is seperating maybe but its sounds like its "abuse" i work at a ski shop and i have experience with people trying to warranty stuff and idk how theyre gonna take it it might be easier to deal with k2 yourself
Take them to your local shop and put them in for warranty. Base material should not separate from the tail. Core shots are not the skis' fault however as thick base material is used on the PRESS than most other brands.
Post pics next time as well, it is easier for people to see what is going on and give you a better suggestion.