For a connected reductive group $G$, we generalize the notion of (semi)stable Higgs $G$-bundles on curves to smooth projective schemes of higher dimension, allowing also Higgs $G$-sheaves, and construct the corresponding moduli space.
"Stable Higgs $G$-sheaves." Rev. Mat. Iberoamericana 24 (2) 703 - 719, July, 2008.