Upon his recent arrival in Australia, His Holiness Dalai Lama was presented with an Australian "Akubra" hat, which holds a place in Australian hearts similar to that occupied by Stetson in the American West.
If you've ever spent any time in Tibet, you know Tibetan people fancy this general sort of design. From this point forward, there is no doubt the hat of choice will be Akubra's "Dalai Lama model."
UPDATE: His Holiness enjoyed this hat very much, and kept wearing it, reportedly remarking, "This is a very practical hat." This hat is considered iconic of Oz, so everyone was quite pleased with his remarks. One woman was even sufficiently moved to present her pet wombat: