We establish a connection between Rokhlin dimension and the
absorption of certain model actions on strongly self-absorbing
-algebras.
Namely, as to be made precise in the paper, let
be a well-behaved locally
compact group. If
is a strongly
self-absorbing
-algebra
and
is an action on a
separable,
-absorbing
-algebra
that has finite Rokhlin dimension with commuting towers, then
tensorially absorbs every semi-strongly self-absorbing
-action on
. In particular, this
is the case when
satisfies any version of what is called the Rokhlin property, such as for
or
. This
contains several existing results of similar nature as special cases. We will in fact prove a
more general version of this theorem, which is intended for use in subsequent work.
We will then discuss some nontrivial applications. Most notably it is shown that for
any
and on any strongly self-absorbing Kirchberg algebra, there exists a unique
-action
having finite Rokhlin dimension with commuting towers up to (very strong) cocycle
conjugacy.
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