Misunderstanding fusion of characters

Question

In section 3 of this paper the author describes the character $\overline{\psi_i\times\psi_j}$ of $G\wr \mathcal{C}_2$ where $\psi_i\in \hat{G}, i\neq j$, and claims that this agrees with the values of $\psi_i\times\psi_j$ on $G\times G$. However, when I try checking calculations myself, I'm finding the degree of each character is double what I expect, and rather than being $\psi_i\times \psi_j(1)$ the degree evaluates to $2(\psi_i\times \psi_j(1))$ for every set of characters where $i\neq j$. What is being misunderstood?

Answer 1

It's explained in the ATLAS that the fusion of two characters $\chi_i, \chi_j$ is calculated $\chi_i+\chi_j$.