How to expose grouping in Views? I have a view, where I use grouping to display publications by year. 
Format: HTML List -> Settings -> Grouping field Nr.1: Year


This is what I get:



Is there a possibility, to expose this grouping to the website user? So that the user can group for example by publications type or author? So the same functionality like exposing filters?
kiamlaluno gave the perfect hint. Without actually using any additional modules, you can just use tabbing for multiple views, each with different grouping.
Thats how you do it:


Create a new view as a page
Page settings -> Menu -> Path -> e.g. /publications
No Menu link





Add a new page to the view with the same credentials like the one above (in my case grouping by field_year) - IMPORTANT
Page settings -> Menu -> Path -> e.g. /publications/by-year (keep the root path)
Page settings -> Menu -> Default menu tab
Parent menu item -> Default menu item





Add a new page to the view with different credentials (in my case grouping by field_type)
Page settings -> Menu -> Path -> e.g. /publications/by-type (keep the root path)
Page settings -> Menu -> Menu tab




Finally there are three pages:



In the frontend it will look like this:



I hope this steps help you a bit. In this way, you can create as many views as you like. 

Thanks to the community again.