Learn Finnish: Tuo iäkäs kirjailija on mainekas. - That elderly writer is renowned.

It comes from the noun ikä (age). When adding the -käs suffix, the root undergoes consonant gradation where the k drops out, leaving the stem iä-. Because the suffix implies abundance, someone with "a lot of age" is elderly.

Why does mainekas use the -kas suffix while iäkäs uses -käs?

This follows standard vowel harmony rules. The root word maine contains the back vowel 'a', so it requires the back-vowel suffix -kas. The root word ikä only contains front and neutral vowels (ä, i), so it takes the front-vowel suffix -käs.

How do words ending in -kas or -käs behave when you add case endings, for example in the elative case?

Adjectives ending in -kas or -käs use a strong stem ending in -kkaa- or -kkää- for most cases (though the partitive just adds -ta / -tä). If you wanted to say "about that elderly writer", the elative forms would be tuosta iäkkäästä kirjailijasta.

How does mainekas differ in nuance from the more common word kuuluisa (famous)?