Grand Kai never actually shows up in the Dragon Ball manga itself, though he gets mentioned. His anime personality? That came straight from Akira Toriyama's suggestions to the production team.
The guy's basically an aged hipster—jeans, denim jacket, always got a boom box blasting rock music nearby. Despite being the trainer of the universe's strongest fighters, he's nothing like a stern master. He's more the sweet, grandfatherly type, similar to how North Kai and Master Roshi act. Grand Kai doesn't care much for formal distance or rigid respect. Instead, he treats everyone around him like equals and basically spoils them like they're his grandkids.
Content compiled by AnimeList.moe from publicly available sources.