A compactness theorem for twisted-unitary elements of integral group rings, with a certified route to the theta-unitary Case A at window B(4) of the Promislow group

Let G be a torsion-free group whose real group algebra R[G] has no zero divisors, and let u -> u^{*theta} be an l2-isometric anti-involution of R[G] (a composition of the inversion involution with a ring automorphism and a sign character). We prove a compactness theorem: for every finite *theta-clos