F-splitting is a notion for algebraic varieties of positive characteristic, which is defined by splitting of the Frobenius endomorphism. Recently, Yobuko has introduced a generalisation of F-splitting, called quasi-F-splitting, via Witt rings. In this talk, we will discuss which algebraic varieties are (should be) quasi-F-split. This is joint work with T. Kawakami, T. Takamatsu, J. Witaszek, F. Yobuko, and S. Yoshikawa.