central leaves in the special fiber of shimura varieties are the loci where the isomorphism class of the universal $p$-divisible group remains constant. the hecke orbit conjecture asserts that every prime-to-$p$ hecke orbit in a pel type shimura variety is dense in the central leaf containing it. this conjecture is proved for hilbert modular varieties by c.-f. yu, and for siegel modular varieties by chai and oort. in this talk i give an overview of the conjecture and present my work that generalizes chai and oort's strategy to irreducible components of certain newton strata on shimura varieties of pel type.