  Over the past years, major attention has been drawn to the question of
identifying Schur-positive sets, i.e. sets of permutations whose associated
quasisymmetric function is symmetric and can be written as a non-negative sum
of Schur symmetric functions. The set of arc permutations, i.e. the set of
permutations $\pi$ in $S_n$ such that for any $1\leq j \leq n$,
$\{\pi(1),\pi(2),\dots,\pi(j)\}$ is an interval in $\mathbb{Z}_n$ is one of the
most noticeable examples. This paper introduces a new type B extension of
Schur-positivity to signed permutations based on Chow's quasisymmetric
functions and generating functions for domino tableaux. As an important
characteristic, our development is compatible with the works of Solomon
regarding the descent algebra of Coxeter groups. In particular, we design
descent preserving bijections between signed arc permutations and sets of
domino tableaux to show that they are indeed type B Schur-positive.
