Can a person file a case of cyber crime against me in another country?

Yes , as per the IT Act, 

If any person without permission of the owner or any other person who is incharge of a computer, computer system or computer network, — 

(a) accesses or secures access to such computer, computer system or computer network;  

(b) downloads, copies or extracts any data, computer data base or information from such computer, computer system or computer network including information or  data held or stored in any removable storage medium; 

(c) introduces or causes to be introduced any computer contaminant or 
computer virus into any computer, computer system or computer network; 

(d) damages or causes to be damaged any computer, computer system or Computer network, data, computer data base or any other programmes residing in such computer, computer system or computer network; 

(e) disrupts or causes disruption of any computer, computer system or 
computer network; 

(f) denies or causes the denial of access to any person authorised to access any  computer, computer system or computer network by any means; 

(g) provides any assistance to any person to facilitate access to a computer,  computer system or computer network in contravention of the provisions of this Act,  rules or regulations made thereunder; 

(h) charges the services availed of by a person to the account of another person by tampering with or manipulating any computer, computer system, or computer Network,he shall be liable to pay damages by way of compensation not exceeding one crore rupees 
to the person so affected. 

Explanation.—For the purposes of this section,— 

(i) "computer contaminant" means any set of computer instructions that are 
designed— 

(a) to modify, destroy, record, transmit data or programme residing 

within a computer, computer system or computer network; or 

(b) by any means to usurp the normal operation of the computer, 
computer system, or computer network; 

(ii) "computer data base" means a representation of information, knowledge, facts,concepts or instructions in text, image, audio, video that are being prepared or have been prepared in a formalised manner or have been produced by a computer, computer system or computer network and are intended for use in a computer, computer system or computer network; 

(iii) "computer virus" means any computer instruction, information, data or programme that destroys, damages, degrades or adversely affects the performance of a computer resource or attaches itself to another computer resource and operates when a programme, daia or instruction is executed or some other event takes place in that computer resource; 

(iv) "damage" means to destroy, alter, delete, add, modify or rearrange any computer resource by any means. 

66. Hacking with computer system.

(1) Whoever with the intent to cause or knowing that he is likely to cause wrongful
loss or damage to the public or any person destroys or deletes or alters any information
residing in a computer resource or diminishes its value or utility or affects it injuriously by
any means, commits hack:

(2) Whoever commits hacking shall be punished with imprisonment up to three years, Or with fine which may extend upto two lakh rupees, or with both
 

He may try to rope you in the above mentioned offences, however, for the purpose he has to file the complaint in India. You have committed a Grave Mistake by Admission of the offence, so if an FIR is lodged in this context, repercussions will follow accordingly.