Where does “elyä” come from?

elyä (Karelian) comes from Finnish -tti, from Finnish -ttää, from Proto-Finnic -ttadak, from Proto-Uralic -kta-.

Ancestry of “elyä”, step by step

Step	Language	Word	Meaning
1	Finnish	-tti	Forms some nouns from verbs, particularly...
2	Finnish	-ttää	Front vowel variant of -ttaa
3	Proto-Finnic	-ttadak	Creates causative verbs from regular verbs,...
4	Proto-Uralic	-kta-	—