input credit of gst paid for rent of branch office

You can't claim that unless the ITC is IGST.

place of supply is karnataka , but there is  no outflow of goods or services. It takes place with in karnataka, so normally this would attract only sgst,cgst . In this case IGST can't be charged.

If you have the IGST invoice , proceed with that. But in this case SGST,CGST should be there. If he gives the IGST bill you can claim the input .

Input Tax Credit is available as per section 16. Mere issue of an invoice by the supplier may not be enough. ALL conditions have to be met. It is also subject to apportionment + blocked credits. Place of supply will not be determined by the invoice of the supplier- if hemakes a mistake then there could be disputes for even the receiver.

Therefore understanding the law as it stands is important. Pl refer to analysis in BGM of idtc of ICAI. idtc @ icai.in [ free] 

Facility of Input service distributor is available for places where one is not registered but pays the local taxes.Restrictions on credit: