The Hebbar Iyengars speak a dialect of Tamil called Hebbar Tamil. This is amixture of Kannada Archaic Tamil and a little bit of Sanskrit. However they are fluent in Kannadaus this as medium to commnicate in public. There are many theories regarding their origin. On eis they are decended form converted Jains of Karnataka. The other that they are local Kanndigas introdused to Vaishnavaite philosophy by Ramanuja. The last is that they descendants of Ramamujans disciples form Tamil Nadu. They us boththe lunar and solar calendars to clebrate various festivals. THey use the solar calendar to clebrate certain festivals eg Nrushima Jyanti. This traditions coincides with the tradition of Srirangam temple Thi ssupports the argument that these people beig direct descendants of Ramanuja's disciples. If they were of Kannadiga descent then why do they speak this dialect of Tamil. instead of pure Kannada.
