Could not resolve android.arch.lifecycle:extensions:1.1.0

You already added google() in the Build.gradle so, try adding the latest version:

implementation "android.arch.lifecycle:extensions:1.1.1"
annotationProcessor "android.arch.lifecycle:compiler:1.1.1"

Also, go to:

File -> Settings -> Build, Execution, Deployment -> Build tools -> Gradle

And uncheck the option if it is checked to download from repository.

In case it didn't help, updating gradle to the latest version will help:

dependencies {
    classpath 'com.android.tools.build:gradle:3.1.4'
}

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