Are terrorists fooling around with muslims ?

A little-known outfit calling itself Lashkar-e-Qahhar has purportedly claimed responsibility for Tuesday's serial blasts in Mumbai.
An e-mail-reportedly from Lashkar-e-Qahhar - to Hindi news channel Aaj Tak claimed the outfit was associated with Al Qaeda and the Pakistan-based terrorist organisation Lashkar-e-Tayiba.
The e-mail said 16 Qahhar activists had carried out the blasts in Mumbai and threatened more attacks if the Indian government does not stop the 'exploitation of Kashmiri people.'
The same outfit had claimed responsibility for the bomb blasts in Varanasi in March this year.

This seems to be another part of Lashkar-e-Taiba.
I fail to understand why do most terrorists turn out to be muslims ? I am not speaking it against any religion, but honestly its a point to be thought about. Why do they use Islam names in their outfits and kill innocent people. Did people of Mumbai who lost lives have anything to do with whatever is problem with Kashmir ?
Does Islam teach killing innocent people ?
Are they abusing Islam ?
Why don't muslims stand out and thwart such enemies of humanity and Islams ?

Earlier some Danish carttonist made an objectionable cartoon of Prophet, muslim organisations stood up to fight it, what about killing of innocent people and that too be people calling themselves true Islamists and use name of Prophet to kill innocent people. Does Islam or did Prophet call for killing innocent people ?