About the regular representation of weak hopf algebra

In the group theory we know $dim_{\mathbb{K}}(\mathbb{K}G)=dim_{\mathbb{K}}(V)=\sum_i (dim_{\mathbb{K}}V_i)^2$ where $V$ is regualr representaion and $V_i$ are irreducible representations. Now consider a weak hopf algebra $H$, then regular representation is a left $H$-module. In Dmitri Nikshych's article arXiv:math/0304098 given a equation $$H \cong \sum_j End_{\mathbb{K}}(V_j)$$ I think this equation means that $dim_{\mathbb{K}}(H)=dim_{\mathbb{K}}(V)=\sum_i (dim_{\mathbb{K}}V_i)^2$ but I do not know how to prove this result.