Banach algebras associated to locally compact groups

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Let G be a group, i.e. G is a set with an associative operation such that each element has an inverse. For example, G may be taken to be the set of numbers, positive or negative, with addition, or the set of orthogonal transformations i.e. a linear transformation followed by translation (the affine group). My research in the next few years will consist of (a) the study of geometric, algebraic and topological properties on Banach algebras associated for G (e.g. group algebra, measure algebra and the Fourier Stieltjes algebra B(G) (b) the study of dual Banach algebras of the corresponding non-commutative function space in the von Neumann algebra VN(G) generated by the left regular representation of G (c) the (non-associative) Jordan structure in VN(G) for the fixed point set of a function in B(G).