He basked in the admiration from his fans, with a happy smile on his face.

basked 是动词 bask 的过去式。bask 原意是指"晒太阳"，引申为"享受、沉浸于某种温暖或愉悦的氛围中"。这里指"沉浸在粉丝的赞美中"这种愉悦感受。