PT Unknown AU D'Angelo, A TI Virtual Localization Formula for Witt Theory PD 10 PY 2023 DI 10.17185/duepublico/79087 LA en AB In this thesis, we extend the Virtual Localization Formula to a wide class of motivic ring spectra, obtaining in particular a localization formula for virtual fundamental classes in Witt theory KW. We extend to general spectra the notions and operations of equivariant bivariant theories. Then we specialise to SL[η-1]-oriented spectra A, obtaining a presentations of A(BN) (where N is the normaliser of the torus in SL2), and an Atiyah-Bott localization theorem for AN(X), for X a scheme equipped with an N-action. Of independent interest, we also describe the ring structure of KW(BN) and give a complete computation of KW-valued Euler classes for all rank two vector bundles over BN. ER