In this paper we study -biprojectivity and character Johnson amenability of some Banach algebras like Beurling algebras and semigroup algebras. In fact We show that L1(G;w) is 0-biprojective if and only if G is compact, where 0 is the augmentation character. We prove that `1(S) is pseudo-amenable if and only if `1(S) is character Johnson-amenable, provided that S is a uniformly locally nite band semigroup. We give some conditions whether -biprojectivity ( -bi atness) of `1(S) implies the niteness (amenability) of S, respectively.
