Background.
Let $G$ be a finite group and $K$ an algebraically closed field whose characteristic does not divide the order of $G$. Let $S_1,\ldots S_n$ be representatives of the isomorphism classes of irreducible representations of $G$. One can show that there is an isomorphism of unital rings $$f\colon K[G]\rightarrow \operatorname{End}_K(S_1)\times\ldots\times \operatorname{End}_K(S_n).$$ Then for $i=1,\ldots n$ the element $e_i=f^{-1}(\operatorname{id}_ {\operatorname{End}_K(S_i)})$ is a central idempotent (aka projector) in $K[G]$.
Now, one can prove that for $i=1,\ldots n$ we have
$$e_i=\dfrac{\operatorname{dim}_K(S_i)}{\vert G\vert}\sum_{g\in G}\chi_{S_i}(g)g^{-1}.$$
Here $\chi_{S_i}$ denotes the character of $S_i$.
My question.
Does the last formula have a name in the literature?
I have seen it referred to as the character-projector-formula, but this terminology seems only marginally used.