We show that the Schur product inside the block matrices over a C*-algebra is a special case of the Hadamard or convolution product inside a reduced crossed product of a C*-algebra by a discrete group. Both products have a very simple Stinespring representation $A \star_h B = V^*\pi(A) S \pi(B) V,$ such that $\pi $ is a *-representation of the crossed product algebra, $S$ is a self-adjoint unitary and $V$ is an isometry, and we will mention some consequences of this. We will introduce the concept, we call, unbounded expectations and show that any reduced crossed product of an injective von Neumann algebra by a discrete countable and finitely generated group posses an unbounded expectation. This extends a result by Lance on the characterization of nuclear C*-algebras.