Relative equivariant covering type equality

Let $X$ be a $G$-CW complex with non-empty fixed-point set $X^G$. Define the relative strict $G$-covering type of the pair $(X,X^G)$ by

$${\rm sct}_G(X,X^G)={\rm sct}(X\setminus X^G).$$

Relative covering type conjecture.

$${\rm sct}_G(X,X^G)+{\rm ct}(X^G)={\rm ct}_G(X).$$

The preceding inequality ${\rm sct}_G(X,X^G)+{\rm ct}(X^G)\leq {\rm ct}_G(X)$ is known; the conjecture asserts that equality always holds.