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Using ultrapowers of $C^{\ast}$-algebras we provide a new construction of themultiplier algebra of a $C^{\ast}$-algebra. This extends the work of Avsec andGoldbring [Houston J. Math., to appear, arXiv:1610.09276.] to the setting ofnoncommutative and nonseparable $C^{\ast}$-algebras. We also extend their workto give a new proof of the fact that groups that act transitively on locallyfinite trees with boundary amenable stabilizers are boundary amenable.

An ultrapower construction of the multiplier algebra of a $C^{\ast}$-algebra and an application to boundary amenability of groups