Projectivity of Certain Banach Modules Related to a Locally Compact Group

Let A be a Banach algebra and let Phi be a nonzero character on A. For a locally compact group G, let the group algebra L-1(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 0-contractibility of A. Furthermore, as a consequence of our result, we investigate the projectivity of some Banach left L-0( )<bold>infinity</bold> (G)*-modules, where L-0(<bold>infinity</bold>)(G) is the Banach space of all essentially bounded measurable functions on G vanishing at infinity.