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We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal homeomorphism of X, and let Y be a closed subset of X. Let u be the standard unitary in C* (Z, X, h). The Y-orbit breaking subalgebra is the subalgebra of C* (Z, X, h) generated by C (X) and all elements f u for f in C (X) such that f vanishes on Y. If intersects each orbit of h at most once, then the Y-orbit breaking subalgebra is large in C* (Z, X, h). Large subalgebras obtained via generalizations of this construction have appeared in a number of places, and we unify their theory in this paper. We prove the following results for an infinite dimensional simple unital C*-algebra A and a stably large subalgebra B of A: B is simple and infinite dimensional. If B is stably finite then so is A, and if B is purely infinite then so is A. The restriction maps from the tracial states of A to the tracial states of B and from the normalized 2-quasitraces on A to the normalized 2-quasitraces on B are bijective. When A is stably finite, the inclusion of B in A induces an isomorphism on the semigroups that remain after deleting from the Cuntz semigroups of A and B all the classes of nonzero projections. B and A have the same radius of comparison., 54 pages; AMSLaTeX

The C*-algebra of a skew-product topological graph is a crossed product of the C*-algebra of the base topological graph by a coaction., minor corrections

We define proper, free and commuting partial actions on upper semicontinuous bundles of $C^*-$algebras. With such, we construct the $C^*-$algebra induced by a partial action and a partial actions on that algebra. Using those action we give a generalization, to partial actions, of Raeburn's Symmetric Imprimitivity Theorem.