Restricting supercuspidal representations via a restriction of data

Let $F$ be a non-archimedean local field of residual characteristic $p$. $\mathbb{G}$ reductive group defined over which splits tamely ramified extension and set $G=\mathbb{G}(F)$. We assume that $p$ does not divide the order Weyl $\mathbb{G}$. Given closed connected $F$-subgroup $\mathbb{H}$ contains derived subgroup $\mathbb{G}$, we study restriction to $H$ an irreducible supercuspidal representation $\pi=\pi_G(\Psi)$ $G$, where $\Psi$ is $G$-datum as per J.K. Yu Construction. provide full description $\pi|_H$ into components, with multiplicity, via data constructs $H$-data from $\Psi$. Analogously, define Kim-Yu types representations $G$ are supercuspidal.