  We provide a systematic and in-depth study of compact group actions with the
Rokhlin property. It is show that the Rokhlin property is generic in some cases
of interest; the case of totally disconnected groups being the most
satisfactory one. One of our main results asserts that the inclusion of the
fixed point algebra induces an order-embedding on K-theory, and that it has a
splitting whenever it is restricted to finitely generated subgroups.
  We develop new results in the context of equivariant semiprojectivity to
study actions with the Rokhlin property. For example, we characterize when the
translation action of a compact group on itself is equivariantly
semiprojective. As an application, it is shown that every Rokhlin action of a
compact Lie group of dimension at most one is a dual action. Similarly, for an
action of a compact Lie group G on C(X), the Rokhlin property is equivalent to
freeness together with triviality of the principal G-bundle $X\to X/G$.
