Tibetan official's summer hat or 'gser theb'. The body is made of lacquered papier mache and is decorated with Chinese and Buddhist symbols. The mounted glass ball on the crown is probably indicative of rank.
A hat of this type ('gser theb') would have been reserved for 'rtse drung' (government officials) and the 'dgon dpon' (treasury administrator who could be a monk or layman). It would have specifically been worn when riding a horse.