  The two dimensional state sum models of Barrett and Tavares are extended to
unoriented spacetimes. The input to the construction is an algebraic structure
dubbed half twist algebras, a class of examples of which is real separable
superalgebras with a continuous parameter. The construction generates pin-minus
TQFTs, including the root invertible theory with partition function the
Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita
invariance of the construction are discussed.
