Equivariant higher twisted K-theory of SU(n) for exponential functor twists

We prove that each exponential functor on the category of finite-dimensional complex inner product spaces and isomorphisms gives rise to an equivariant higher (that is, non-classical) twist of K-theory over G=SU(n). This twist is represented by a Fell bundle E→G, which reduces to the basic gerbe for the top exterior power functor. The groupoid G comes equipped with a G-action and an augmentation map G→G, that is an equivariant equivalence. The C∗-algebra C∗(E) associated to E is stably isomorphic to the section algebra of a locally trivial bundle with stabilised strongly self-absorbing fibres. Using a version of the Mayer–Vietoris spectral sequence, we compute the equivariant higher twisted K-groups KG∗(C∗(E)) for arbitrary exponential functor twists over SU(2), and also over SU(3) after rationalisation