Although Grand Kai does not appear in the Dragon Ball manga, he is mentioned there. In fact, his characterization in the anime was suggested to the production staff by the manga's author Akira Toriyama himself.

Grand Kai is portrayed as an aged hipster, usually wearing jeans and a denim jacket, and constantly listening to rock music on his boom box.

Even though he is the teacher of the greatest warriors in the universe, Grand Kai is more of a sweet and a kind grandfatherly figure than a traditional disciplinarian (much like North Kai and Master Roshi). Paying no heed to respectful-but-cold formality, he lovingly treats his social-inferiors as equals and dotes on them as if they were his own grandchildren.

(Source: Dragon Ball Wiki)