So for a example a effective /cheap battle group could be like this..
1 x Gorshov Class Frigate using S-400s 150km++ range ,Kalibers,torpedos with 1 Ka-27 Helicopter, escorted by
2 x Gremyashchy-class corvette with S-400s small range and Kalibers.. with 1 Ka-27
2 x Steregushchy-class corvette using Shtil-1(Buks)sam defenses + Oniks with 1 KA-27
4 x Buyan-class small patrol boats with 8x Kalibers each and Igla sams .. 2 x AK-630 gatlin gun defenses.
6 x Project 22160 small Patrol boats ,Underwater mortars ,sonars ,Igla missiles and with Ka-52 hellicopters
armed with Aesa Radars ,with 80x S-8 rockets + Vympe 2x R-73M2 air to air missiles with 40km range + 4x igla missiles.
Don't let the armament fool you into thinking these boats are something they are not... a decent storm in the atlantic and the Buyan class and Project 22160 would be sunk.
A carrier battlegroup would not be sunk by a frigate and a group of corvettes... if it really was that easy then there would be little point in larger ships.
Russia does need cruisers and carriers if she wants to have a modern mobile navy.
To suggest she can get by with very well armed Frigates because they are cheaper and more mobile and can be bought in larger numbers is like saying there is no need for the PAK FA... for one PAK FA you get a shtload of Yak-130s... put a big AESA in its nose and use AWACS and space based radar and have them all carry R-37M 300km range AAMs and nothing the enemy has will get close...
If the Army is your thing... replace all the MBTs with those light special forces jeeps and don't bother with conventional army forces... just have all spetsnaz...
A navy without a carrier is like an Army without an Air Force... it can still fight but not as well... it will not see as well, it will not reach as far, it will not kill as many bad guys and it will take more casualties in most things it does.
A decent Russian carrier group will include at least one carrier and two cruisers.. preferably a Kirov based vessel and a Slava based vessel.
The Carrier will have all offensive missiles removed and only have SAMs and CIWS... it will have a lot of them.
The cruisers will have enough land attack and anti ship missiles to sink 5 enemy carrier groups and a few countries.
The Aircraft on the carrier will have a critical anti sub mission, a critical anti air mission and a secondary anti ship and land attack mission with aircraft carrying long range cruise missiles.
There will be about 6 multi role destroyers and potentially a Mistral class helicopter carrier depending on the missions... when there is a mistral carrier attached extra ships will be added too, plus all the support vessels.
Frigates will be left at home to patrol local waters as will all patrol boats.
There will be a few Yasen and upgraded Oscar II subs to round out the carrier group along of course with support ships and reloading ships etc.
Remember the Sigma C4IR system will integrate all the data from all the platforms of the fleet and space and surface and subsurface vessels to create a picture of underwater, surface, air, and space around the group in real time.