In General Relativity the objects transform under the general linear group GL(3,1).
Does this include fermions? If you rotate an object around $360^{\circ}$ the fermions inside the object will not be the same until you rotate it round another $360^{\circ}$.
So what is the generalisation of GL(3,1) to fermions? Is it GL(3,1,C)? or something else? I presume it must have SU(2)xSU(2) as a subgroup.