Equality of relative radii of comparison for fixed-point and underlying algebra in a specific Z/2-action

Establish whether, for the stably finite simple unital C*-algebra A equipped with the Z/2Z-action α described in the paper’s Example 5.8 and for any nonzero positive element a ∈ (A^α)+, the equality rc(Cu(A^α), [a]) = rc(Cu(A), [ι(a)]) holds, where ι: A^α → A denotes the inclusion.

Background

Example 5.8 considers a specific stably finite simple unital C*-algebra A with an action α: Z2 → Aut(A) from [7], for which the authors derive an inequality chain relating the radius of comparison of the crossed product to relative radii for the fixed-point algebra and the underlying algebra. In this setting, Theorem 4.11 shows rc(Cu(A^α), [a]) ≤ rc(Cu(A), [ι(a)]).

The open question asks whether these relative radii coincide in this particular example, potentially sharpening the comparison results between the fixed-point algebra and A via the inclusion map.