Karnataka GSTN will be raising tax-invoice for 'Business Promotion Services' provided to Chennai Chennai of same legal entity and not that for 'Renting of Immovable Property' or 'Hotel Accommodation Services'.
Hence, Place of Services for above services so provided will be Chennai & NOT Karnataka because 'Business Promotion Services' provided by Karnataka GSTN is NOT directly in relation to an immovable property.
Provision of above service (i.e. 'Business Promotion Services' from Karnataka to Chennai) is the reason for which said tax-payer has taken separate registration at Karnataka, as can be seen from given factual scenario.
Valuation of such services can be kept on lower side using second provision to Rule 28(1) of the CGST Rules, 2017 (i.e. when recipient distant person i.e. Chennai Chennai of same legal entity, is entitled to full input tax credit against gst so charged by Karnataka GSTN).
It is legally permitted choice of the taxpayer to chose lower valuation under GST for its 'Business Promotion Services' (by not including other costs like salary, housekeeping, hoteling, electricity & so on consumed by Karnataka GSTN while providing business promotion services to its Chennai GSTN and its profit margin thereon) in the given situation.
This legally permitted choice is a not a benefit extended to the taxpayer in real sense as same is given to the fact that having higher taxable value and higher tax-liability on Chennai GSTN is revenue - neutral for Govt. as recipient (i.e. distinct person) is entitled for 100% ITC. However, having 'legally permitted choice' means Dept's officer has got no choice but NOT to question valuation in given situation.
These are ex facie views of mine and the same should not be construed as professional advice / suggestion or recommendation.