How to specify "own type" as return type in Kotlin

There's no language feature supporting this, but you can always use recursive generics (which is the pattern many libraries use):

// Define a recursive generic parameter Me
trait Foo<Me: Foo<Me>> {
    fun bar(): Me {
        // Here we have to cast, because the compiler does not know that Me is the same as this class
        return this as Me
    }
}

// In subclasses, pass itself to the superclass as an argument:
class FooClassA : Foo<FooClassA> {
    fun a() {}
}

class FooClassB : Foo<FooClassB> {
    fun b() {}
}

You can return something's own type with extension functions.

interface ExampleInterface
// Everything that implements ExampleInterface will have this method.
fun <T : ExampleInterface> T.doSomething(): T {
    return this
}

class ClassA : ExampleInterface {
    fun classASpecificMethod() {}
}

class ClassB : ExampleInterface {
    fun classBSpecificMethod() {}
}

fun example() {
    // doSomething() returns ClassA!
    ClassA().doSomething().classASpecificMethod()
    // doSomething() returns ClassB!
    ClassB().doSomething().classBSpecificMethod()
}