Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...