Lateral tabs related shortcuts

I love the lateral tabs feature and the tab groups as well, I use it a lot at my work place.

However, there are at least a couple of keyboard shortcuts that should be added in order to improve the user productivity:

• a shortcut to open a new tab in the group the current tab belong to: when I'm working with the tabs from a given group, is like I'm working with that group, and if I open a new tab, it's very likely I want to open it in that very group. 
• a shortcut to pin/unpin lateral tabs

It goes without saying that for users who need to maximize their productivity it makes a big difference to be able to carry out the most frequent tasks by means of keyboard shortcuts.