Simple, they want independence for Chechnya. Make the cost of not giving in so gruesome and ugly that Russian popular opinion simply says "Make it go away, it's not worth it".
It's a complex situation and Putin needs some serious buy-in from the U.S. and Euro's to give him more leeway in dealing with this. This might just give it to him.
Innocents get caught in a global pi$$ing contest. Ugly.. Ugly.. Ugly...
Prayers for the victims and their families.
"they want independence for Chechnya"
I don't think you have been paying a lot of attention to the world around you.
The independent Chechnya would be an Islamofascist state where they could train and export terrorists just line Afganistan, Just like syria, Just like Iran.
They pretend this is about independence so that they can be called freedom fighters, they are not freedom fighters they are Islamofascists hell bent on murder.