sorry i didn't find solution ...
in my site i add text item in search
i create an item link to my k2 category + set item id + choose a template
but i don"t understand i am redirect to result page with good template ..
i miss something ?
In your case, when you click on some suggested item in text field, it makes redirect directly to K2 item (not K2 category page). Can you provide an example links with the same K2 item but different templates?