Most Chechens are just worn out. You say the Chechens should handle it. Chechnya is ruled by Russia. The Russians want it that way so they have to handle it. they are the authorities.
The politics of that area is very complicated. The Chechens were deported by Stalin and returned later.
They have several groups that don't like Russian control but not all are these kind of terrorists.
Many Chechens don't like the Russians but could accept Russian rule if they had some control over their lives.They don't necessarily want to be ruled by terrorists.
It is very complicated. You can read some of the different Chechen perspectives at www.rferl.org They have articles about this.