  In superstring theory spin structures are present on both the 2-dimensional
worldsheet and 10-dimensional spacetime. We present a new proposal for the
B-field in superstring theory and demonstrate its interaction with worldsheet
spin structures. Our formulation generalizes to orientifolds, where various
twistings appear. A special case of the orientifold worldsheet B-field
amplitude is a KO-theoretic construction of the Z/8Z-valued Kervaire invariant
on pin-minus surfaces.
