  In this paper we study the regularity of the Szeg\"o projection on Lebesgue
and Sobolev spaces on the boundary of the unbounded model worm domain
$D'_\beta$.
  We consider the Hardy space $H^2(D'_\beta)$. Denoting by $bD'_\beta$ the
boundary of $D'_\beta$, it is classical that $H^2(D'_\beta)$ can be identified
with the closed subspace of $L^2(bD'_\beta,d\sigma)$, denoted by
$H^2(bD'_\beta)$, consisting of the boundary values of functions in
$H^2(D'_\beta)$, where $d\sigma$ is the induced Lebesgue measure. The
orthogonal Hilbert space projection $P: L^2(D'_\beta,d\sigma)\to
H^2(bD'_\beta)$ is called the Szeg\"o projection.
  Let $W^{s,p}(bD'_\beta)$ denote the Lebesgue--Sobolev space on $bD'_\beta$.
We prove that $P$, initially defined on the dense subspace
$W^{s,p}(bD'_\beta)\cap L^2(bD'_\beta,d\sigma)$, extends to a bounded operator
$P: W^{s,p}(bD'_\beta)\to
  W^{s,p}(bD'_\beta)$, for $1<p<\infty$ and $s\ge0$.
