Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness

Disproves Kaplansky's quasitrace conjecture by constructing a separable unital complex C^∗-algebra admitting normalized 2-quasitraces, all of which are nonadditive. As a consequence, two unital simple stably finite C^∗-algebras can have a properly infinite minimal tensor product, with one factor $C_r^*(\mathbb F_2)$.