Invariants Associated to Orthogonal ε-constants

In this paper we use the theory of $\epsilon$-constants associated to tame finite group actions on arithmetic surfaces to define a Brauer group invariant $\mu(\X,G,V)$ associated to certain symplectic motives of weight one. We then discuss the relationship between this invariant and $w_2(\pi)$, the Galois theoretic invariant associated to tame covers of surfaces.