Other depictions:
A sketch
Ganesh artwork showing a swastika on his hand
Hindu gods take on a lot of 'roles' but Ganesh as remover of obstacles (and Shiva as Lord of the Dance) is one of my favorites.
ETA: Typically he has a right handed swastika as it is 'creation' vs (left handed) 'destruction' Not that the left handed swastika is 'evil' in Hinduism, destruction isn't an evil act, but part of life, but it can be 'misfortune'
/had it backwards the first time