As per section 10(1)(b) of IGST Act, the place of supply of goods, other than supply of goods imported into, or exported from India, where the goods are delivered by the supplier to a recipient or any other person on the direction of a third person, whether acting as an agent or otherwise, before or during movement of goods, either by way of transfer of documents of title to the goods or otherwise, it shall be deemed that the said third person has received the goods and the place of supply of such goods shall be the principal place of business of such person.
As per this Section, even if the goods are directly delivered to the SEZ unit by the vendor of Karnataka & the invoice is raised in your name, it would be deemed that the goods were delivered to you and then supplied to SEZ.
The Vendor from whom you purchase the raw materials will charge you CGST & SGST of Karnataka.
Further as per Section 16(1) of the IGST Act, supply of goods or services or both to a Special Economic Zone developer or a Special Economic Zone unit is treated as Zero Rated Supply.
You may Supply Goods or Services or both under LUT without payment of IGST or you may supply goods or services or both on payment of IGST and claim refund of such tax paid on goods or services or both supplied.