Banach spaces with a basis that are hereditarily asymptotically isometric to l1l1 and the fixed point property

We show that there is an equivalent norm in a Banach space with a basis which is hereditarily asymptotically isometric to l1l1 such that every subspace has in turn a subspace with the fixed point property. Also we give an example of a family of non-reflexive spaces not isomorphic to l1l1 having the fixed point property and other related examples.