On the calculation of UNil

Cappell's codimension 1 splitting obstruction surgery group UNiln is a direct summand of the Wall surgery obstruction group of an amalgamated free product. For any ring with involution R we use the quadratic Poincaré cobordism formulation of the L-groups to prove thatLn(R[x])=Ln(R)⊕UNiln(R;R,R).We combine this with Weiss' universal chain bundle theory to produce almost complete calculations of UNil*(Z;Z,Z) and the Wall surgery obstruction groups L*(Z[D∞]) of the infinite dihedral group D∞=Z2*Z2.