Monfared defined θ-Lau product structure A ×θ B for two Banach algebras A and B, where θ : B ! C is a multiplicative linear functional. In this paper, we study the notion of left φ-biflatness and left φ-biprojectivity for the θ Lau product structure A×θ B. For a locally compact group G, we show that M(G) ×θ M(G) is left character biflat (left character biprojective) if and only if G is discrete and amenable (G is finite), respectively. Also we prove that ‘1(N_) ×θ ‘1(N_) is neither (φN_; θ)-biprojective nor (0; φN_)-biprojective, where φN_ is the augmentation character on ‘1(N_): Finally, we give an example among the Lau product structure of matrix algebras which is not left φ-biflat.
