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This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.

Mathematics. --- K-theory. --- Functional analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- K-Theory. --- Functional Analysis. --- Global Analysis and Analysis on Manifolds. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebraic topology --- Homology theory --- Math --- Science --- Global analysis.