In this paper, M. Romagny defines for an action of a group scheme $G$ on a stack $X$ the fixed point stacks $X^G$ associated to the group action on a stack and in Theorem 3.3 he proves that if

1. the group $G$ is proper and flat of finite representation
2. $X$ is a Deligne-Mumford stack

then $X^G$ is algebraic. Later in this note, he proves that condition 2. can be relaxed to $X$ being algebraic with the diagonal being locally of finite presentation.

I am mostly interested in actions by complex tori on algebraic stacks locally of finite type. In this case, one doesn't have the properness from condition 1. Is it still true that the stack of fixed points $X^G$ is algebraic?

Another question that I am interested in, is what happens if one considers higher stacks and torus actions on them. Are there some results regarding this?

In this paper, M. Romagny defines for an action of a group scheme $G$ on a stack $X$ the fixed point stacks $X^G$ associated to the group action on a stack and in Theorem 3.3 he proves that if

1. the group $G$ is proper and flat of finite representation
2. $X$ is a Deligne-Mumford stack

then $X^G$ is algebraic. Later in this note, he proves that condition 2. can be relaxed to $X$ being algebraic with the diagonal being locally of finite presentation.

I am mostly interested in actions by complex tori on algebraic stacks locally of finite type. In this case, one doesn't have the properness from condition 1. Is it still true that the stack of fixed points $X^G$ is algebraic?

I am aware that it is common to take fixed points of Deligne-Mumford stacks as in Graber--Pandharipand with respect to the torus action, but the same approach doesn't seem to work in the completely general case.