  In a recent paper, DeBacker and Reeder construct and parameterize L-packets
on pure inner forms of unramified p-adic groups, that consist of depth zero
supercuspidal representations. We generalize their work to non-pure inner
forms, by providing an alternative construction based on the theory of
isocrystals with additional structure due to Kottwitz. Furthermore, we show the
stability and endoscopic transfer for these L-packets.
