Let A be a Banach algebra and let ϕ be a nonzero character on A. For a locally compact group G, let the group algebra L1(G) be a closed two-sided ideal in A. In this paper, we aim to relate projectivity of some Banach left A-modules and the ϕ-contractibility of A. Furthermore, as a consequence of our result, we investigate the projectivity of some Banach left L∞0 (G)∗-modules, here L∞0(G) is the Banach space of all essentially bounded measurable functions on G vanishing at infinity.
