Faceted search results as MENU_LOCAL_TASK tab

Is there a way to make the faceted search results page (using a display style of a view) appear as a local task tab under an existing menu item 'xyz'? I was hoping to set the faceted search env base_path to xyz/search and somehow set it to a local task menu type (as one can do for views), but cannot figure out the way to get this effect.

Thanks for any pointers.