Where do the Australians keep the ashes when they win them?

Answer 1

Although the "Ashes" are won and lost, the urn normally remains in the Marylebone Cricket Club Museum at Lord's (London). A replica is used to "hold up" in Ashes matches - it is the symbolism of winning (and the history that goes with it) that matters not the actual original ashes urn which is too precious to move around.

Thus in answer to your question, the Australians keep them at Lord's.