Direct sum of group representations ($R\oplus S$)

For group representations $R:G\to GL(V)$ and $S:G\to GL(W)$, their direct sum acts on the direct sum of vector spaces by $(R\oplus S)(g)(v,w)=(R(g)v,S(g)w)$. Its character and Dynkin index, when defined, are the sums of those of the two summands.