Here is something interesting to note as there are two Ganapati/Ganesha here... one is Buddhist and the other is an opponent to Buddhism. I cannot verify this but if someone can it would be great!
Apparently Buddhist Ganapati is not the same as our Ganesha (son of Parvati, and Shiva). He is totally different. He is a Tantric Buddhist Ganapati named as Avalokiteshvara who after killing the Hindu Ganesha then cut off the elephant head and placed it on top of his own, thus taking on the appearance of the defeated Ganesha! Ganapati has an ambivalent status in Buddhist tantra. The Hindu form is often seen as an opponent to Buddhist practice. Some particular distinction are, the Buddhist Ganapati uses the seed syllable GAH, not the Hindu seed syllable for Ganapati, which is GAM.
Ganesha and TibetGanesha Scriptures were translated into Tibetan and introduced in Tibet by the monks by 10 and 11 c. Though based on Indian Scriptures Ganesha acquires a very different form outside India. For Tibetan and Tantric Buddhists, Ganapati is the Sanskrit name commonly used and the word found in Tibetan literature too. The two words Ganesha and Ganapati have the same basic meaning in English: lord of Ganas.
In one Tibetan form he is shown being trodden under foot by Mah?kala, who is a Dharmapala (“protector of dharma”) in Vajrayana Buddhism (Tibetan Buddhism and Japanese Shingon Buddhism). Mahakala (Shadbhuja) in the six-armed form is also an emanation of Avalokiteshvara. In this form he stands atop an elephant headed supine figure. The name of the figure varies from ritual text to ritual text but is commonly referred to as Vinayaka. As the Buddhist god Vin?yaka, he is often shown dancing, a form called Nritya Ganapati
Ganesha was worshipped in Khotan, Endere, Kashgar and Lobnor. Four-handed Ganesha images of these countries have been found. They are shown with modaka (sweet), axe, goad and radish. He was famous for killing demons and was thus a deity of protection. In many temples he was shown as dvarapalaka also. He had both male and female forms (Ganesha and Ganeshani). Not only he was shown with a radish, but his mouse also had a radish in its mouth. Such Ganesha images have been found at Mongolia.
Source:
http://theemerald.wordpress.com/2009/03/19/buddhist-deity-ganapati/