From the Super Mario Wiki
Bowser's Shell is a Special Item exclusive to Mario Kart: Double Dash!! that only Bowser and Bowser Jr. can receive; however, King Boo and Petey Piranha can also receive it, being able to use any racer-exclusive item. It is a gigantic shell that, when released, bounces around the track like a normal Green Shell, toppling any kart that it hits as well as knocking down the items they hold.
After Bowser's Shell hits the walls of a course roughly fifteen times, the shell breaks apart. Unlike many other items, the Bowser Shell can resist being destroyed by some other items, and even bounces off another special item should it collide with one.
It is unknown if these are just weapons used by Bowser modeled after him, or actually his spare shells. The item reappears as one of Bowser's items in Mario Kart Arcade GP 2.
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